The solution to this may not be immediately obvious, so it's necessary to understand what GIT is doing under the hood.
When you have a git-svn checkout, git maintains the svn repository state in a remote branch. You work within your local branch and commit changes locally. When you're ready to commit back to SVN you'd normally just do a "git svn dcommit".
If you make some local git changes and commit locally, then do the dcommit that is rejected by a pre-commit hook, then normally in SVN you would fix the error locally and re-try your commit. In GIT the commits have been separately checked-in locally, so GIT will try to commit each change separately to SVN - but this won't work because the first local commit was rejected by SVN.
The solution is to create a new git branch, forked from the current branch just before your rejected commit. To do this you would first want to look at "git log" to get the commit hash from git, then create your new branch and change to it:
$ git log
# find the commit hash you're after
$ git branch temporary_branch 68b8976ba0944
$ git checkout temporary_branch
$ git merge --squash dd7354fcd397 7f5e78f7e737ed4 5e07bf3c6f5c15
$ git svn dcommit
You'll then want to go back to your local master git branch, and likely clean up after yourself:
$ git checkout master
$ git svn rebase
$ git reset --hard HEAD
$ git branch -D temprorary_branch
Disclaimer: You'll want to check the last "reset --hard" and "branch -D" commands do lose anything before running them. I.e. don't do anything here without understanding it first!