How can I modify a backup? I'm backing up my mac from a Hard Drive that someone gave to me, but I don't have enough space on my Mac. How I can delete files that I don't need to be backed up (when I try to delete it says The operation can’t be completed because backup items can’t be modified) from the HDD so backup wont be corrupted and I can backup my Mac?
You cannot delete files from a Time Machine backup specifically, but you can exclude things from the backup...


Go to System Preferences > Time Machine
Click Options
You will be presented with a list you can add and remove folders to be excluded like this:




By removing things like Applications folders and cloud storage services like Dropbox, OneDrive and Google Drive you can save a lot of space.

If this still isn't working you need a bigger drive to backup to.