My aunt wanted to help me repair a room in my house and wrote me a check. She is very sharp and mentally competent, yet faily members are upset.

Your profile says ur caring for someone who has age decline. Are you helping Aunt in her own home? Are you being paid for it? If there is no Dementia involved, then she did this as a gift and she can do it.

How did the family member find out Aunt wrote you a check?

If you are accepting money from someone impaired, then yes, you can be accused of elder abuse.
The truth is that your aunt should not be gifting large amounts of money she cannot afford to family members. She may thereby impair her ability to get, for instance, Medicaid help if it is needed in her future care.

If your Aunt is competent, that is to say has no impairment at all, then she is perfectly capable of deciding WHAT she wants to do with her money, including sadly giving it away to scammers. But that doesn't make it a morally right or good thing.

I want you to look at "Medicaid look back rules regarding gifting" and see if this could pertain for your Aunt say five years in the future. If so, I feel it is morally wrong for you to accept this money, and would be good for you to educate your aunt as regards gifting large sums of money, when it may work against her in the future.
As to whether or not you can get into LEGAL trouble, again, if your aunt is competent in her own decisions and affairs I fail to see how you could be held legally responsible.
That wouldn't stop the relative from accusing you and reporting you to APS. If the visit you are simply honest with them.

Just had an afterthought. Do you think Aunt is giving you money to repair the room because she may later want to move in with you?

That's not how it happens. That relative would need to hire an attorney and prove there is fraud (because your Aunt is writing the check voluntarily).

Is your Aunt very elderly? Is she very wealthy? If she's elderly, she's on a fixed income and unless she has robust assets, needs to be prudent about where she spends, but if you say she is competent then it's her decision to make. However, you're not a doctor so "competency" is assessed by different types of testing. One feature of dementia is that people lose their ability to make good judgements. This may not have been a good judgment in her best interest.

Does your Aunt have a PoA?

My mother’s BF’s daughter kept threatening my mother with legal action and putting liens on her house because BF helped pay for a handicapped bathroom that mom installed in her house for him. He was over 90y/o and perfectly cognizant.

Mom went through a lot an anxiety and many sleepless nights. However, the daughter didn’t have a leg to stand on. A competent person can spend their money any way they want.

It’s all about the threatening family member wanting money for themselves.

She wrote you a check wanting to repair a room in your house? Or was it her house you did the work for?

Highly doubtful..Arrested for what? Prepare an invoice clearly indicating the services you rendered, payment for these services and very hopefully get your aunt to sign it. This is not a situation that police are likely to even consider nor is really under their jurisdiction. Family member would likely have to hire a lawyer and pay for one and even then the lawyer would have to feel there was a case or be taken to the cleaners by a lawyer who would just amass charges. It would likely prove a bitter headache for family member.

You might provide a little more details just to enlighten those who also may have opinions for you with this matter.