what you have is a classic example of someone adding something to the boat without any forethought as to what happens when it needs servicing.... this is done way too often by way too many people.........:bang:
the fiberglass is tough. it has a non skid pattern that will have the adhesive in the rough pattern of it... a real pain to get clean.
you are going to have to get a sharp scraper and try and get under it to lift it up.... depending on what the installer used, a lubricant like WD40 may help the scraper cut in to the adhesive, as if its something like 3M 4000, it will kind of grab the blade and not allow it to be scraped or cut too easily. lubricating the blade will almost always make the task easier....
if its something like liquid nails they used, your kinda on your own there as I dont know of anything that will get thru that stuff except a grinder...
on our 25, the PO used 3M non slip tape on the cabin floor, and the adhesive on that stuff is some of the best available, especiaslly when it gets into the non skid pattern of the floor... after I got down to just the adhesive left, I found easy off over cleaner would cut it faster and better than any other high powered solvents available, as the really good solvent would flash off too quick and it would leave the glue residue smeared, whereas the easyoff oven cleaner dissolved it, and it remained dissolved and liquefied so I could wipe it up off the floor....
you will probably end up cutting a piece of carpet to overlay the messed up floor after you get the damaged wood out of it..... best of luck.