How do you handle submitting previously published material? Do you mention it was published before (in this case, it was a print publication)? Does that help or hurt?

I have a story that got some praise and mentions by reviewers of an anthology. While the anthology is still available for purchase (print-on-demand, 2 years old), the sales have fizzled out, and the publisher, a one-man show, actually died soon after its publication.

It was a non-paying publication with a standard contract for first rights of print pub. Does that mean I have to mention where it was first published? I'm not looking to be deceptive. Just wondering if previously published material with some media attention might help in getting the piece into a journal with a wider reach. Or, if editors wouldn't consider it because it's already had its day. The story is a retold fairy tale, which seems to have a decent market.