Leaving out Frozen Tilapia
Please see this thread for general storage questions (edit: and this thread for questions related to leaving food at room temperature).

Since the fish had been sitting in an open, unrefrigerated sink for what sounds like several hours, I would generally regard it as unsafe by this point.  Putting it back into the refrigerator would not sufficiently inhibit the growth of any bacteria that made their way into the fish during that time.  But there is no way to know with absolute certainty.

I'll take a cue from rumtscho's answer to another safety-related question and note that we can't tell you here about what you should do.  Kitchen professionals generally err on the side of caution, but you must make your own decisions about the risk involved, and whether that outweighs any qualms you have about waste.