I was just wondering if you can do any harm by deleting old back up file made by Links, located in the admin/back-up dir?

The dated backup files are just that - backups made each time you build.
The current links database files are in the data directory.

If everything is running fine and you don't suspect any problems, you can delete the files in your backup directory. My recommendation would be to keep the most recent two sets (links, categories, email, etc.) I personally download all my backup files just in case and keep them for a month, but this is because right now I'm on a fast connection. There are (or possibly were) mods by Widgetz and others to automatically zip and delete your backup files.