Re-grouting old kitchen counter tile
 

We just moved into a home with a kitchen that has tiles for counter tops. The grout was really dirty, so upon some suggestions I used oxyclean and a toothbrush to clean it. The grout was sooooo gross with caked on grease. Uh oh... afterwards, the grout crumbled off and now there are big holes in the grout and/or sections missing. It looks like we might have to remove the grout altogether and refill it. My husband has done kitchen floor grouting, but not counter tops so he's a bit wary.

What's the best way to remove the rest of the grout, and what products are the best to refill the grout line? We have a dremmel tool, and access to home depot/lowes and a specialty home improvement store. I guess I can order online too. Any help would be appreciated.
Attachment 56291

That is unsanded grout---it is very soft----usually the grout is removed with a utility knife---that space is to narrow for a power tool---

Use unsanded gout to fill the gap----