I closed a joint checking account of mine and mom's too soon. I received 2 small amount checks in her name. Do I have to go through court and probate these checks?

Bookluvers idea is great. I’d try that first if it fits.

If not depending on probate types & costs may not be worth doing. BUT if they are not cashed they could go to dead accounts division of your State Treasury. I think checks from insurers, financial institutions, funeral homes must go to state treasury which in turn can deposit.  And then after a period of time are fully redeemable by heirs. My state - Louisiana- did redemption days a few years ago with TV spots and newspaper ads on what to bring to establish heirship. Also had online list by name and amounts paid. There were oodles of checks out as so many had undelivered mail post Katrina for years. Huge success. For New Orleans area it was at Lakeside Mall and the lines were out the building. The checks issued by State Treasury in the presenting heirs name & good for 90 days or back to treasury.

I know it’s not the same situation exactly like yours. This was what I did.....
My mom received a reimbursement check from the ambulance services. I could have just deposited into our joint account and withdraw the same amount for myself. But my conscience bothered me that it was not right. The check was for her. She’s no longer alive. I went online to my personal bank account, printed the 2 checks I paid for her bills, attached copies of the payment receipts and mailed everything back to the ambulance company. I explained the situation. I paid for mom’s bills, can they re-issue new checks under my name?... They did.
I’m not sure if the company of those checks will do the same for you. They would need backup documents on why they should change names on the check.... Wouldn’t probate be expensive? Or not in your area?

Unless there had been an account opened which said "the estate of your mother's name", I don't think that you would have been able to deposit those checks for her into that joint account. I ran into this myself. I did not think about going to probate court. You can try going there.