I did some serious research earlier this year, serious enough to use several different research assisting AI's, and found that under the law, unless these 'aliens' are actually human, these are seen as no more than animals with no hunting restrictions so as long as you abide by the general hunting laws of your area there is nothing wrong with hunting them for trophies or other uses in the United States.
Not so with Bigfoot though, they're a protected species in some places and in Skamania County in Washington State you could actually get a thousand dollar fine and maybe a year in jail on top of it for hunting one, so be careful that these aliens aren't of the Bigfoot species before you take one as a trophy.
