Solid Hardwood, Engineered and Laminate Flooring - Hole in Floor

Hi! I have purchased a home that was built in the 50's and have taken up the carpet in one room to reveal oak flooring which is in great condition and we plan on refinishing. Now my dilema is in our living room/hallway there is oak under the "scuzzy" carpet but in one section there is a unfinished spot adjacent to the heating register. The register will not cover the area completely. The best I can describe it is it looks like a small grid with no hardwood on top of it and I can see down to the floor. My query is what is this called(I am a newbie) and what can we do to fix this. Can we take some pieces out of the closet or buy some replacement pieces we are sort of at a loss..I have never seen this before. I don't think that a heating register will fit over this area. Why was this left like this..maybe they repaired or ran out of materials? Thanks in advance.