You could try something like this (`bash`):
shopt -s nullglob
for i in *\'* ; do mv -v "$i" "${i/\'/}" ; done
This uses shell string replacement. You probably don't want to glob files that don't have `'` in them since the `mv` would fail. Without the `nullglob` option, the glob pattern itself would be passed to `mv` if there are no matching files.