Can't delete old Time Machine backups from Trash
I fixed this by using tmutil delete.
First, I changed directory into where all the trashed backups were being kept:
cd /Volumes/MacBook\ Pro\ Backup/.Trashes/501

Then, I checked all the files in the directory to make sure I knew what I was deleting. This showed me a list of folders named by date:
sudo ls

Afterwards, I was able to use tmutil delete to delete all the backups:
sudo tmutil delete *

From now on, whenever I want to delete old backups, I will use tmutil delete on the backup folder.