I accept that quilts can be less than perfect and that they age with time, I rarely go back and do anything to any of my own projects. I can also accept that sometimes I take old tops from the thrift store and do things with them. Or, the quilt I made my hubby (we met on the internet, it was for before we were together) that he pretty much destroyed the vintage fabric I used for the back and simply quilted a new back with a different design over the whole thing.
Anyway, if the problem is that you only followed the grid of the squares something easy like that, sure you can take out the stitching if you want. Or... you can carefully lift up the fabric from the back, cut a slit in it and grab out as much of the bad batting as you can. You can then leave the fabric there or carefully snip around, leaving maybe 1/2" around the quilting lines. That's the solution I've found for 6-12" grid lines and baggy batting.
Then you can put on a fresh piece of batting along with a new back, just a back, or maybe just a layer of flannel in-between.
Sometimes all you can do with a well loved quilt is use it as batting for the next one, but you do need to deal with the lump factor and in your case your top is still worth working on/keeping it going in the future.
I don't generally use old quilts as batting but I have more than once especially when taking a cherished blanky and incorporating it hidden into an adult top or for other sentimental/personal reasons. It's still there, our little secret just the quilter and the recipient need to know.