During a commit, I'm not clear on what the behavior is when you check or uncheck a checkbox next to a file that was deleted. See image.
Checking the check box means that you include the change in the next commit. For example, checking a modified file will tell TortoiseHg to commit the modifications of the file. It is also possible, in newer versions of TortoiseHg, to cherry-pick the individual changes within the file itself, by checking the differences in the right-side panel.
For the removed file, it is the same thing. Checking the file tells TortoiseHg that the removal of the file has to be taken into account in the next commit, so the file will be removed in the commit. Leaving it unchecked, on the other hand, will prevent the file from being removed in the repo, and the file will remain as an uncommitted change after the commit.
And finally, if you check an untracked file, TortoiseHg will add it in the repository for you in the next commit.