Deleting of old backups in Time machine
The sparsebundle is a disk image file and probably contains your Time Machine files. If you double-click it, it should be mounted. If not, launch Disk Utility and open it from there (File > Open Disk Image...). 

In order to delete backups, enter Time Machine, select a snapshot (time) and right-click in the Finder window. From there you can delete the snapshot by clicking Delete Backup. Watch out no more confirmation will be asked! You can also delete all backups / snapshots of a file or folder by selecting Delete All Backups of ....

If you are more the Terminal kind of person you can also use tmutil. This would look somewhat like this:

sudo tmutil delete /Volumes/Time_Machine_Disk/Backups.backupdb/computer/date/


You should only use these methods and not delete files manually from your mounted sparsebundle image.