I think my turning point when I have to turn it in is $50, so I'd keep this one. Especially if it's worn.
If it's a wallet or something like that, or a bigger sum, I'd turn it in, though.
But like stated, it's old and worn.. and I wouldn't want that money to get so lonely out there...
They're probably afraid, scared, maybe even in a panic. I couldn't stand that. I'd have to do something. I'd have to pick them up, warm them up, and give them a nice, gently home in my wallet, where they'll be nice and safe against the warm, leather walls. Not like there's any other money in there, so the two $20 bills will have each other, in a warm home, with no one else to bother them.
They'll spend a nice few days, cuddled up together, relaxing, maybe having a nice chat with my credit card or drivers license. Maybe even a few new bills would accompany them and they could have a nice little party. Enjoy themselves and have a grand time.
Then the day would come when that money simply must be spent. But since the bills were found together, I'd wanna keep them together. So I'd probably go out at some point and go food shopping and make sure to buy at least $40 worth. I'd reach the register and give the cashier the two $20's, a little afraid of where they were headed.They'd suddenly find themselves stacked up with other bills, and excited to see so many familiar faces!
The two bills would get to know their new friends over the course of the next few days, and meet new friends as they're added into the mix. They'd become good friends with some, best friends with others, meet some strange, new friends called 'coins', and have even more fun times.
Then the day would come when that money has to go to the bank. The bills would be strapped into bundles and taken quite a ways. They're not afraid, though, because they're surrounded by the friends they've made over the days. The money would eventually end up in a large bank vault, filled with friends, and new friends to make. A massive vault filled with money and endless amounts of fun to be had. The bills would be so happy. They have each other, their friends, and endless possibilities.
...Er, might have gotten a bit off-topic there.
But yeah...
tl;dr: I'd keep it.