How to teach modern manners to an 81 yr. old man with dementia?

You can't teach too much of anything to a person with dementia. They are incapable.

Instead of dodging strategically she should say, unsmiling,"Mr Smith, don't take hold of me please because it makes me feel very uncomfortable. Thank you."

Get a male massage therapist and see what happens.

She is the professional in this situation.
SHE is the one that should have said/indicated from the start that a hug and kiss is not appropriate or professional.
Redirections could be a start:
Maybe she, after the massage have dad sit down and have a glass of water. (hydration highly recommended after a massage) and while he is having his water she can leave.
If this will not work then she needs to pull the "professional card" and as he approaches for the hug and kiss she could put out her hand to shake his and then turn and leave.

I am sure this is not a matter of "teaching today's norms to an old guy with dementia" I am sure he never hugged or kissed the person that cut his hair, the nurse that drew blood, the cashier at the store. This is a matter of with dementia filters are dropped or lost and people do things, say things that they did not before.
If all else fails you can take dad by the hand and walk him to his chair or to the table for a snack while the massage therapist leaves.

How sad it is that we can no longer give someone a hug or even a simple kiss on the cheek without people getting all bent out of shape over it. I mean really? I can only guess it's because this is a younger women and it grosses her out because he's an older man.
The way you described it sounds like it's just a simple hug and kiss of appreciation and nothing more or nothing sexual.
And you say that you must support the massage therapist, but how about supporting your dad, who's brain is now broken and is doing his very best.
If the therapist is really that uncomfortable, tell her not to come back, and like said hire a man to give him a massage, since your dads behavior seems to upset you too.
I hope that doesn't mean that you don't let him give you a hug and a kiss
occasionally.

And P.S. and by the way. I am only 63 years old with no dementia and I am a die hard hugger. I hug ALL my friends, family members, and lots of folks in my caregivers support group who occasionally just need a good old fashioned hug.
This world would be a much better place if more people gave and received hugs. I'm just saying.

She is a therapist.
So, no, you don't need to intercede.
She needs to decide when you act for herself, by herself.

I don't believe it is your place to teach today's norms to your Dad. And dementia patients don't make excellent students.

This seems to me an incredibly simple thing for the therapist to handle, and if she chooses not to address it that is up to her.

That was never OK, so he should have learned before he had dementia. Now it's too late.

Get between him and the therapist, or get a male to do the job instead.

Why can't this therapist leave the room as soon as she is finished? Then make sure she is somewhere else when he is ready to leave. I would say if she is young, she does not like being kissed and hugged by an old man. And by the way, he does not see himself as an old man.

Let the massage therapist deal with this situation by quitting the job if she's so uncomfortable with your father.

Teaching an elder with dementia new "manners" is like trying to teach a 1 year old Algebra. Isn't happening and totally unrealistic expectation on your part, unfortunately.

I suggest you read this 33 of booklet online about managing dementia and what to expect with an elder who's been diagnosed with it.

Understanding the Dementia Experience, by Jennifer Ghent-Fuller 
https://www.smashwords.com/books/view/210580

Jennifer is a nurse who worked for many years as an educator and counsellor for people with dementia and their families, as well as others in caring roles. She addresses the emotional and grief issues in the contexts in which they arise for families living with dementia. The reviews for her books are phenomenal b/c they are written in plain English & very easy to read/understand. Her writings have been VERY helpful for me.

The full copy of her book is available here:

https://www.amazon.com/Thoughtful-Dementia-Care-Understanding-Experience/dp/B09WN439CC/ref=sr_1_2?crid=2E7WWE9X5UFXR&keywords=jennifer+ghent+fuller+books&qid=1657468364&sprefix=jennifer+ghent%2Caps%2C631&sr=8-2

Good luck! 

Is this an inappropriate hug and kiss on the cheek or just an aversion to being touched by an 81 year old?

If he or she, I can't tell because they are referred to as both in your post, can not deal with THEIR personal boundaries being invaded, it is time to find someone that can.

Sorry, I have no sympathy for the massage therapist, they are professionals and should be able to deal with these situations. My lands, they handle someone's naked body for 30, 60, 90 minutes and then can't handle a sincere thanks with a quick hug and kiss on the cheek?!? Instead it's made into some sideshow? Yea, nope! Find a professional that knows how to keep the boundaries.

You cannot teach someone with dementia and you can’t expect them to retain anything you tell them.

Elderly people do not change their ways at 81. Someone with dementia certainly isn't going to.
The message therapist can tell him not to touch her or she can request to boss not have him as a client. Guaranteed if some big blond guy called Sven or Eric is doing his message he will not try to hug and kiss him good-bye.

No way. You cannot teach him anything because his “learning” resources are being progressively lost.

If you cannot arrange for a qualified male therapist, it is your responsibility to be ABSOLUTELY CERTAIN” that he never “wins”.

If you are present (watching) you and she must coordinate her exit so that he is unable to get near enough to her to initiate the inappropriate behavior.

Cut sessions shorter, have her walk away without announcing that she’s finished or leaving.

If he is “persistent” it means that her “departure” is taking too long.

Part of this is her responsibility, and definitely SHOULD have been part of her training. SHE needs to be using departure skills that she may have not learned yet.

(Massage for dementia patients is wonderful by the way!)

I had a similar situation trying to teach my father that washing hands after using the bathroom was a requirement. And this was back when he was still pretty with it. I had to treat him like a 6 year old and ask him if he washed his hands every time he left the bathroom. And every time he would have to turn around and go back in.

Sadly, your dad can’t reason anymore. You’ll have to run interference or change to a male for the massages (which may cause another set of issues, given dad’s age, man touching a man, etc) Don’t waste energy trying to teach dad, just decide how to best prevent

You can teach until you are blue in the face, but your dad has lost the ability to learn manners. Due to his dementia, he's now operating on his primal/sexual instinct.

You will have to stop ihim.
Tell him firmly NO.
Get between him and the therapist.
Pull him out of the room.
The therapist should leave promptly before your dad even has a chance to act.
Switch to a male therapist.