Replacing filler in hardwood floors
Google "bowtie inlay" for details on what's possible. You can do the work either with chisels or a router (or both). And, for what it's worth, bowtie isn't the only shape out there... it's just reasonably charming and has straight lines that make it more manageable for chisel work. (Sharp chisels are always good, but particularly good in this instance.)

Anyway, the black would be chiseled or router-ed out; a small replacement piece would be glued in; then you'd have to sand it flush and apply a local finish similar to the existing. You wouldn't have to refinish the whole floor. 

Almost all cutting tools are dangerous. If you don't have experience with a router, please read up on what can go wrong and practice on scrap.

The not-very-nice-in-my-opinion alternate is to chip out the black and use a lighter coloured wood filler. The really bad thing about this is that your wood's pores might (depending on the finish) collect traces of filler that'll make the whole repair look messy. And, as mentioned, the colour of filler is uniform, so it'll jump out at you as well.