I believe the usual English style is "gift wrap" (two words) when used as a compound noun ("I bought a 100-metre roll of gift wrap.") and hyphenated when used as a verb ("Please gift-wrap this.")

Please gift-wrap this.

At least one dictionary doesn't say so, but Oxford (British English) does.

http://www.learnersdictionary.c...on/gift%20wrap

I actually debated on which to use when I submitted this one and googled a bit before making a decision. However, I've changed it.

That's interesting, CK. Yet another case where U.S. usage varies from British usage. I mostly use the Canadian Oxford Dictionary, which follows British usage most of the time, except on a few oddities like "tyre" for U.S. and Canadian "tire" and "boot" for the trunk of a car. The other one that Canadians differ from the Brits on is spellings like "analyze" (U.S. and Canadian) versus "analyse" (British). Noah Webster tried to rationalize and simplify spelling, but most of his suggestions were not adopted outside the U.S. The crypto-fascist Colonel Robert McCormick for a while tried to get his own spelling changes adopted, and he famously forced his Chicago Tribune to spell words like "thorough" as "thoro," for which he was widely ridiculed.