How to delete another machine's time machine backup?
You can use the tmutil tool to delete backups one by one.
sudo tmutil delete /Volumes/drive_name/Backups.backupdb/mac_name/YYYY-MM-DD-hhmmss
If you are sure you have selected the correct name, you can delete all backups from that one Mac by not passing in the time and letting it delete the entire folder:
sudo tmutil delete /Volumes/drive_name/Backups.backupdb/mac_name
The sudo command needs your password (and it won't echo to the screen, so just type it and pause to be sure you're dating the correct files before pressing enter).