If you're trying to rely totally on the file name for the date, then something like this:
TODAY=$(date '+%s')
for f in /backup/*_repo.svn.gz ; do
DATESTR=$(echo $f | sed "s/^\/backup\/\(.*\)_repo\.svn\.gz/\1/")
FILEDATE=$(date -d "$DATESTR" '+%s')
if ((FILEDATE + 7*24*60*60 < TODAY)) ; then
rm $f
fi
done