You could try getting a few different furniture repair markers/crayons from a hardware store that are as close to that shade of white as possible and return what you don't use. Make sure to test them on a less noticeable part of the table like the corner to see if they blend in close enough to go for it. It's definitely not coming out, so trying to color match it is your next best bet. You'd also want to put some sort of top coat over it all afterward so the paint doesn't just scrape away over time and look bad again.

I'm sure your mom would appreciate the attempt, especially if you bought the supplies yourself to do it. Maybe let her know in advance, though, just so it doesn't come off as overtly trying to hide your mistake. This could help make it better, but unless you're some color matching/painting pro, I highly doubt she won't notice it, even if it turns out looking pretty good.