There's not a thing wrong with regifting. You might want to think, though, about the $20 part, only because I have heard other people in work gift exchanges, and family ones too, come to think of it, about what they called "the gift value arms race", where people go over the $10 limit, and then other people feel badly, so next time THEY go over the $10 limit...etc.
"My predominant feeling is one of gratitude. I have loved and been loved;I have been given much and I have given something in return...Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and an adventure." O. Sacks