Hello Jaybird and Welcome to the Forum:
The plywood clips are a substitute for the tounge and groove method of keeping the plywood from moving between the two pieces in the space between joists. This is usually a treatment for roof decks. If your subfloor is 3/4" thick and the joists are spaced on 16" centers, I would take a side-grinder and grind the exposed tops off the clips. However, if your subfloor is thinner or the joists are spaced wider, you may need a complete new subfloor over the existing; use 3/4" tounge and groove underlayment grade OSB glued and screwed down. (Glue the T&G also.) Now you have a slick, smooth, strong floor ready for anything you wish to cover it with.
I found years ago that builders were adding the layers of subfloor together and claiming nice, strong floors. For instance I was in one house where the builder used 7/16" OSB and covered it with 5/8" particle board and claimed to have a floor over 1" thick. The particle board is not designed for structural use and the thin OSB is like walking on cardboard. I wish you well with your project and ask that you post back with pictures to let us know how it went.