Another way of dealing with this situation if your files ARE already checked in, and your files have been merged (but not committed, so the merge conflicts are inserted into the file) is to run:
git reset
This will switch to HEAD, and tell git to forget any merge conflicts, and leave the working directory as is. Then you can edit the files in question (search for the "Updated upstream" notices). Once you've dealt with the conflicts, you can run
git add -p
which will allow you to interactively select which changes you want to add to the index. Once the index looks good (git diff --cached), you can commit, and then
git reset --hard
to destroy all the unwanted changes in your working directory.