Trust your gut.
Could be her guilt, could be manipulation. But $50 for a 7 year old child??? Clueless at best, bribery at worst.
Put the money in a savings account for the child - it won't make much interest but it won't have fees. Write a thank you saying what happened and why. Small tokens are okay as gifts but tons of money are meaningless. Your thank you can say "I put it in the bank until she is old enough to appreciate a gift of that size". I wouldn't highlight that she doesn't know this grandmother, but if you're pushed, you may have to. This woman has no RIGHTS to the child. If she really cares, she will write you and say she wants to stay connected, and what is a good gift that is in line with your child's interests. Your answer should be for a $10 or $15 gift, maybe a book, or perhaps a subscription to an age-appropriate magazine subscription. Impersonal, maybe. But a magazine comes every month or every other, which is not a bad way for a distant person to stay in the child's life.
I'd say very little right now unless/until you get a lot of mail from her. If you do, open it first to see if it's appropriate for your child. None of this "mail fraud" nonsense - she's a minor and you have the right. If you ask what she wants from you, it's kind of antagonistic and could make her even more pushy. (I don't blame you for questioning her motives, mind you - I'm just not sure you should say so."
Make a small response, and then don't do anything else and see what happens. If you are contacted again, then you can decide based on the type of contact, frequency, etc. And if there's more money involved, I'd say you don't allow your child to have that kind of cash at her young age and either it's going in the bank for her college education or you'll have to respectfully request that it stop.