100 year old bungalow in Wisconsin. Maple floors in kitchen and bedrooms, Oak in Dining and Living rooms. I've tried every method recommended to properly clean the floors. Doesn't matter what type of mop or rag I use (micro-fiber, spin-mop, t-shirt, cloth diaper, etc). Regardless, my wiping tool will collect little chips or splinters of either the wood or the sealer between the wood with every wipe. It's enough that even when wiping with a cloth diaper in a 4' x 4' area I have to take the rag to the trash can to hand pick out the little chips to avoid them scratching up the floor surface or clogging up my washing machine.

I've looked through every one of the I Have Problems posts, and am dumb-founded that no one else has reported this issue. I'm at the point where I only wipe up small drips as they come up, and avoid cleaning the floors altogether to avoid further damage. It's getting warmer out now, and the humidity makes the floor stickier than I'd like. I really just want to get the surface cleaned up better.

Where the chips come up, they leave light colored voids in the finish, so I just can't keep ruining the look of the floor.

I believe what's coming off is older sealer or glue that's between the boards. But I'm no expert, so hoping for some advice here.

I'm a renter, so I don't want to risk damaging the owners beautiful floors.

Appreciate any guidance you can offer.

I think that the newer varnish film has an adhesion problem. Old floors that have been coated with another new coat of finish that dries but doesn't stick to the old varnish will separate because the old floor was either not prepared correctly or the new finish was not compatible with the old finish.
An old floor must be cleaned well for any new coating to adhere. After cleaning the surface must be treated so the new finish has some tooth to stick to the old finish.
Usually the preparation will include a light sanding to scuff the surface.
The chipping may not happen for a week or more after the coating was applied. Stress like walking on the floor or sliding something over the surface will start an area to come loose.
The floor will need to be refinished after sanding through the finish that is chipping or peeling off the surface. Best results are for sanding to bare wood.
You did not cause the problem.