Sorry to hear about your costly mistake. You're a better man for admitting it, and an even BETTER one for wanting to 'make it right'. I, too, do hope you're much more successful at something you're much more skilled at.
Sometimes, tiles-depending, you can use an ice chopper. First, you need to sharpen it a bit. I use a fine-toothed file to get the burrs off. (Always work BOTH sides of the edge.) Then, I sharpen it a bit. As you 'run' the chopper UNDER the stuck tiles, you should be able to get a lot of it up. DO be careful of gouging the wood underlayment. As long as the damage isn't too bad, you needn't worry about 'leveling' the underlayment since you're installing cement backerboard. FLIP the chopper as you go so you work both sides of it evenly. Keeping the edge 'clean' and sharp helps. Again, be careful of gouging the underlayment.
Other than that, you're on your own. My best to ya and hope this helps.