If one wants to remove the target version on a single bug, one can use Edit and then select, from the top of the dropdown list of of targets, the empty line. This works well.

But if one selects multiple bugs and uses Update Target Version (at the bottom of the View Issues table), the same dropdown list appears, but selecting the empty top line generates error "Please select an item in the list". Thus there's no way to a empty multiple target versions (except one at a time using individual edits).