'Screening' refers to using an abrasive screen to go over the floor.

It will dull the finish.

A screen on the sander (instead of sandpaper) helps preven the sanding dust from getting caught between the abrasive (on the screen or paper) and the floor.

It is more important for lightly sanding the finish since there is enough heat generated from the sanding to melt the dust and make it stick to the finish and really mess things up.

The dust can move through the holes in the sanding screen instead of being trapped between sandpaper and the floor.

At one time, I managed a dozen rental properties. I often had floors screened between tenants so a new coat of polyurethane could be applied without reducing the life of the hardwood. Of course, when tenants put out their ciggies on the floor, even sanding wasn't enough to eliminate the burns. It's "character", said my flooring guy.

After the floor's screened, you can switch to semi-gloss rather than high-gloss if you want.

In my previous home, we had our hardwoods screened, which as worthy stated, allowed them to recoat our polyurethane. In our case we didn't have any floor damage, we just had areas where the poly had worn down. It was inexpensive and effective.
Diane

Screen 'em and put down more polyurethane. The last coat should be satin instead of gloss, to get the look you want. I believe gloss polyurethane is considered to have slightly better adhesion and protective properties. Satin poly is just gloss with some sort of optical duller added. It is completely compatible with gloss, and standard practice to just use it for the last coat if that's the finish you want.

I am just repeating, imperfectly, what I've read about polyurethane elsewhere. If you want a technically exact explanation, do a search on the woodworking forum.

" Satin poly is just gloss with some sort of optical duller added."

Very fine silica (sand).

It it is not kept in suspension uniformly during application the finish can have uneven gloss.