Mike, great picture good resolution....what smart / stupid phone do you use.
Also, do you think if there is the usual 4-6 coats of floor finish that the latex backing will still have penetrated all the way to the base tile?
Meaning.....stripping it with semi aggressive black pad to the base tile remove the residual backing.
Obviously if there is no finish or only 2 coats this theory won't be plausible.