You have no tax reporting requirement.
If this is your mother's only income, she does not have a reporting requirement since the amount is less than her standard deduction of $12,300. The only reason she would be required to file a return is if she is married and her spouse files a US tax return as married filing jointly (in which case they must list all their combined income); or she is married and her spouse files as married filing separately and chooses itemized deductions. (In that case, she must also file, report the income, and choose itemized deductions even if her deductions are zero.)
You would then need to report the $500 on line 1, with "HH" next to it indicating household employee. This may be listed under "uncommon income" or it may require a manual entry. But as explained above, it is likely that she simply is not required to file.
Important!! I just realized that if your mother has a green card and a valid SSN, she is probably eligible for the $1800 stimulus payment, so she will want to file a tax return this year. That means you will report the babysitting wages even though it won't be taxable. I think I saw @Hal_Al or @rjs had an explanation of how to enter household employee wages in Turbotax when there is no W-2.
Also important!! The IRS will not direct deposit a refund for her unless she has a US bank account in her name and SSN. The IRS will not deposit her refund into your bank account. If she does not have an account, she can request a paper check. It can be mailed to her in India and she can deposit it there, or maybe it can be mailed to you and you could forward it to her. You could request a debit card, but it would have to come to you in the US, and I don't know the best way to transfer the funds to her after that.
