There was no formal contract or agreement. At some point she will need to apply for Medicaid. Will they consider that a gift? And if so, really? Can an agreement be drawn up now for what went on in the past?
That is not a gift. That is rent that includes food, utilities, and care. You can prove that she was living in your home at your address. That is not a gift.
You should find out what the Medicaid "lookback" period is in CT, Here in MN it's 5 years. You state in your profile that your mom has dementia/ALZ. Does this mean you are her durable PoA and it is active? It may be worth the investment of a 1 hr consult with an elder law attorney who knows Medicaid planning. I don't think you can retroactively create a contract even if she didn't have dementia/cognitive decline.
Yes, if your mother gave you money for groceries, etc. not much of a problem. Rental? A problem. Would have had to be claimed on your taxes. I am guessing you didn't. Without a formal agreement this may be called into question. However, 1,000 a month is not unreasonable for room, board and care, so you may be able to work this out if you kept good track of the payments Mom gave you and what they are for, and if they were regular. I would see an Elder Law Attorney in your State. It is now too late to address any of this, and you can hope Mom won't need help until it passes into the distance of 5 year lookback; otherwise, when it is time and you have this question I would pass it by an attorney.
I would suggest setting aside whatever documentation you can gather as to where the money went in case you need it later.
$1,000 a month could have been her contribution towards the household's bills: groceries, utilities, eating out, transportation, maybe rent.