using TM after a SD Restore
 

Apple sent me a new replacement iMac because of a technical issue the original machine was having.

No problem, I use SD. So, I boot from my external SD drive and copy to the new computer. Things are working fine but for my TM. The new computer, which has the exact same specs and all the data is the same, will not use the existing Time Machine backup to write to or read from. So as it is now, I've lost all the TM history.

Is there anyway around this or do I just have to start a new TM backup?

It doesn't have anything to do with the SD! restore: it's a different Mac, and it typically won't re-use the same TM backup.

If all of the source data (most importantly the machine name) is the same, you should be able to re-select the backup partition in Time Machine and it'll parse all the old backups. I do this every week when I rotate backup drives.

Since the Mac is actually a different one, with a different ethernet address, I don't think that's going to work.