All paperwork, approval processes and stamps must be as before. Theyll also probably try to tack on a processing fee.
It was pushed past the Parliamentarian because it was a tax, but years ago they have learned that fees can be tacked on and they can be justified to get around the constitutional complaint.
Since the fee isn't a tax, the director of the agency can put it in place by saying they are just covering the cost of conducting the background check without increasing taxes on those who don't participate.
Since it is a fee that pays for the costs of transferring the item only, it is not a tax that requires House action or can be argued as a hurdle in exercising a protected right.
Since agencies can do so much internally and under wraps it takes vigilance to hold them in check. That is why those looking to strip rights love agencies.