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I did a little testing with this feature. First I destroyed my Cat Carrier (Siamese) and a few other companions I obtained from vendors. There was no option available to relearn any of them. Next I deleted my Panda Collar and a few other blue items. I got the usual dialogue box where I had to enter the word "delete" to confirm my decision. Unfortunately, I could not reclaim these pets either.
UPDATE: Based on my testing along with what I've heard from others, there are only four pets that can be retrieved when lost (all are quest rewards):