I'd probably keep it around for a while, if for no other reason than I'm a collector, and I hang on to the different, the odd, the unusual. If it's a contemporary counterfeit, it's a good one, and thus worth keeping. The question is part of the charm.
1896-O VAM-22 is one of the less-obvious vintage counterfeits, although it does tend to come in higher grade than the other VAM-listed "privately made" coins. $50 for a VAM-22 in that grade is a pretty good deal.