Recovering and Continuing a Time Machine Backup?

Before I sold my MacBook Pro I backed it up using time machine as I'd been doing for the past eight or so months. In the interim between owning computers my data safely sat on a 3tb external hard drive waiting to be restored in time. The day finally came a week ago with my latest purchase (an iMac) and it was restored beautifully, almost too perfectly. Even the tabs I'd had open on my old computer were waiting to be revisited in Chrome, color me astonished. I took my time updating apps, buying new apps, and generally doing all the new computer set-up stuff I normally do, although my computer already knew all my passwords and so the process took about an hour rather then all day. However when I activated Time Machine on my new computer it doesn't want to continue using the backup system it was restored from (allowing me access to eight months worth of backups). Now it's not THAT important because everything exists on my hard drive, but it would be nice just in case I deleted something six months or so to have access to it, a la time machine. I love Apple, I love how things "Just Work" but when situations of this ilk happen it's a total bummer.

Any ideas' or should I just over-write the old backups and start anew?