a thing given willingly to someone without payment; a present.So, "free gift" is like "wet water".
But even worse is "free gift with purchase". No. Sorry. If you have to buy something then anything else you get is not free because you paid! This manages to be redundant and contradictory at the same time.
Yet, "free gift" is used quite a lot. Google ngram viewer lets us track its use in books and, after a long decline, it seems to be making a comeback. But "free gift" is mostly not used in books. Simply Googling "free gift" (on October 9, 2016 at 9:30 Eastern) came up with 29,700,000 hits! Some of them were not really uses of the phrase (e.g. "free gift cards"). And "free gift with purchase" came up with 1,480,000 hits!
What words and phrases annoy you?