First off, regifting isn't a bad thing. I know for a fact Pope John Paul II was a regifter. So if the vicar of Christ can regift that's good enough for me. Nearly every teacher I know is a regifter. I'm a regifter. So long as you follow a few simple rules to avoid hurt feelings and embarrassment regifting can be a great thing. Here's how to do it...
1) Remove any name tags that would give it away as a regift! I can't believe that needs to be said but I can't tell you how many gifts I've gotten with someone else's name on the gift tag. Look all over for tags and stickers.
2) Make sure it's clean. This means the package is free of dust, in the original box, seal unbroken, and the box is in good condition. Rewrap the gift in new paper. If the gift is in a gift bag or box make sure those are in excellent condition. Gift bags themselves are often reused so there is a tiny bit of flexibility there. However, if you've had the item sitting in a gift bag or gift box in a closet somewhere then inspect the bag/box for bugs that may have crawled in there and died. Yup, that happens. I once got a glass bowl that was placed in a gift box. By the time I got it there were a few dead moths in it AND a gift tag that said, "To: Laura".
3) Make sure it's something that can be regifted. Don't regift handmade or personalized things. Sweaters your crazy aunt knit, books with inscriptions on it, monogrammed items, etc are all ineligible items to regift.
4) Regift into a different social circles. Don't regift something a co-worker gave you to another co-worker. The idea is to give the gift to someone the person who gave it to you probably will never bump into thus avoiding hurt feelings.
5) Have the regift make sense. Yes, whatever it is you probably just want out of your house but the idea is for people to not guess it's a regift. Don't give the bubblebath you got from your neighbor to your 18 year old nephew. Don't give the wine glasses to someone who doesn't drink. Think about peoples' interests, otherwise, the item is going to become another regift.
6) Use Yankee Swaps. So long as it's outside of the original gifters circle a Yankee Swap or White Elephant can be a great and fun way to get rid of regift that you just can't find a home for.