These are designed to soften and partly remove the old finish without stripping it completely.
The only really satisfactory way of repairing the damage is to remove the old finish and then treat the burnt area.
But most amateurs can remove the finish from ordinary items without worry.
Remove only the finish that lifts off easily.
If it removes the finish, follow this treatment with 100-grit paper to complete the job.
You will have to remove the old finish and strip the floor down to the bare wood.
What would you recommend to remove the textured finish, and what kind of primer should I then apply?
If you do not remove the old finish, then you will have to continue applying the same type of coating used before.
But if the 80-grit paper removes the finish, follow it with 100-grit paper to complete the job in two stages.
The only remedy in this case is to remove the finish down to bare wood and try a commercial bleaching agent.