You have basically killed the TM backup. TM backups look like real files if you look at the drive with Finder, but the reality is that they are mostly just links to files that are elsewhere. Those links are chained together through the backups to provide the ability to resurrect previous versions when you do a restore. The entire thing is managed like a very complex database. By reaching in directly through Finder, you have broken the links, leaving files lost and the backup unreliable. Links are very small files, which is why when you deleted the links you didn't save a lot of storage. At this point about all you can do is reformat the TM drive and do a new full backup. All your history will be gone (actually, it's gone already).
For the future, the only way to delete TM backups is through TM. You open TM go back in time and then use the Finder-like window to navigate back to the oldest backup, select the files you want to remove and delete them from the backup. All the links will be updated and the integrity of the backup will be maintained because TM will update the links.
You can stop reading now, but I'll give a bit more on how TM works below:
When you make the first backup, the real files are copied over to the backup drive as they are. When the next backup is done, the files that are NOT changed are not copied again, but links are created to the real file from the first backup. Links are very small pointers that look like files in the Finder window, but just point to where the real file is. Files that are changed are copied over as they are. On the next backup (the third one), again unchanged files are linked, but this time to link goes to the link in the second backup, which links to the original backup. That is done so that when you say you want a file from the second backup the links work. Changed files are copied over completely. In the fourth backup, files unchanged from backup three get links to the backup three file or links. Changed and new files get copied. Repeat this process over and over and you end up with some long chains of links for files that have not changed and some short chains for files that are more volatile and some new real files. At the end of a period of time, TM does an intelligent pruning of the links to summarize certain files in the backup. For example, after a week, hourly backups are compressed to one per day. Eventually backups are compressed more by editing the links to have one per week. The logic is that you are more likely to need a file changed in the last day or so than to have to reach back into months ago, and if you DO go back months, the file is unlikely to have a lot of volatility, so a relatively good copy from one week should do. TM then updates all the links so that as you go back in time, you can find the real data for that particular instance of the backup.
For a more graphic presentation of how TM works, see this:
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Bottom Line: You cannot make changes in TM backups through Finder as Finder does NOT update the link chains. Only TM does that.
