A poly finish will wear away in high traffic areas like the entrance way to your home. Even if the guy did a perfect job, after 20 years in high traffic it will wear away.
However, I don't know exactly what you mean by "warn off on the edge" In my house, I have to redo a 2 square foot area of parquet oak wood floor in the dining room from wear by the opening to the kitchen. The finish is completely warn off as well as the stain in this area. Not just on the edge, so I don't know what you mean.
I have extra parquet squares as well. Save them in case something like pet urine completely ruins one or more parquet tiles.
The important thing I am considering is what type and color of stain. I must match the existing stain in my dining room as closely as possible, then apply a fresh coat or 3 of poly. I will use the hardwwod floor cleaning product made by Bruce Flooring for poly surface floors. This stuff really cleans away any dirt. Probably about 3 or 4 cleanings, and I will be ready to stain. Once I stain, I will apply first coat of poly, then screen sand down any raised grain, poly again, steel wool, and final coat of poly. I will use satin finish to match the rest of the floor.
Please describe the exact extent of your damage & others may be able to help more percisely. Remember that we cannot see your floor, so the better you describe your situation, the better we can help.