Script to remove specific strings in file name

Without the rename tool, using a simple shell loop with parameter substitution to rename a file at a time:

for name in /path/to/dir/*_[rR]elinked_new_*
do
    newname=${name##*/}
    newname=${name%/*}/${newname#*_[rR]elinked_new_}

    # or:
    # newname=$(basename "$name")
    # newname=$(dirname "$name")/${newname#*_[rR]elinked_new_}

    mv -- "$name" "$newname"
done

Inside the loop, the value of newname is first computed as the filename component of the name variable (the last bit after the last slash in the pathname).

The newname variable is then modified by pretending it with the directory path and the result of removing whatever text matches the shell pattern *_[rR]elinked_new_ from the start of the filename.

The code can be simplified somewhat by first changing the current directory into the directory where the files are located:

cd /path/to/dir || exit

for name in *_[rR]elinked_new_*
do
    newname=${name#*_[rR]elinked_new_}
    mv -- "$name" "$newname"
done

This is really just a comment in response to your problem with "Argument list too long", but it started to look messy in the comment box, so now it's an answer. :)

The reason you're getting that error is that * tries to put every file in the directory onto the command line, which has length restrictions. Instead you can loop over the files (or use find to do a similar thing) and call rename on each individually:

find /path/to/dir -iname '*relinked_new_*' -exec prename 's/[0-9]+_[rR]elinked_new_//' {} \;