Can a dementia patient remember inappropriate sexual behavior and then apologize for behavior?

You cannot explain or reason with dementia. They lose filters, say and do inappropriate things. They don't even understand that a behavior is not acceptable or why they should apologize.

You can only control and manage your response. Realize it is the disease. Check with the doc to see how to possibly reduce the behavior.

Women will also misbehave.

It sounds like you suspect that, dementia or not, this person knew quite well at the time that the sexual behavior was inappropriate, and that is why they apologised. If that’s right, and you feel generous, you could give them one more chance. After that, curtains. You may want to check out the extent of their dementia, because it can come to the point where they don’t know what they have done or that it is inappropriate. Unless they’ve reached that point, old age does not give old men a licence to misbehave.

Does the “patient” remember and or apologize for other things that he/she has done?
If the person spills a glass of water, on purpose will they realize it was wrong and will they say they are sorry? If they make a mean remark, or act out do they say they are sorry?
Sometimes in an early stage there might be an occasion where this might be possible but often the “filters” that restrain us begin to fade.
Now I am going to maybe walk on thin ice here.
If this is a person you are caring for that in the past or even now is expressing inappropriate behavior to you or other member of the household for your own mental health you can freely step back and let someone else care for this person.
If this is a new behavior talk to their doctor. There are medications that might help. And there is also the option of placing this person in a Memory Care facility.
You should do what needs to be done for your safety.

Maybe they can realize their behavior and the inappropriateness of it in the early stages when they still have much of their faculties in tact. Later in the disease dementia robs them of the ability to know what they've done or to apologize for it.