I checked on summoner with regain, and I can't remember what result I found...
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Regain is easiest. If you aren't wearing caller's neck, you can check your <pettp>. I just wish I could remember what the hell I found (yeah, informative). If I go again on Summoner I will have to check.
I remember never being able to find information on atmacite affecting pets (which I assumed it did but no where could I find text saying it did) until I tested it myself, and it does work. I almost think that boons don't work on pets, but again I'll double check.
Sorry for the month delay on this, but I finally had the chance to test if pets received the grimoire boons.
The short answer is "no".
We completed Sauromugue Champaign's Researcher 1 once, for the +5 Auto-Refresh boon. I then geared up PUP/SCH, and pulled out my lil' Aurelie in BLM mode. After entering the same Burrow again, I summoned her, and told her to nuke away to her heart's content. She had no auto-refresh at any point. I, on the other hand, did. I was leader both times, and made sure that the boon was enscribed on my grimoire before entering the second time. Since I highly doubt avatars and jug pets are treated differently than automatons...
Well, all I can do is call shenanigans on the Dev team for backsliding on this! After making sure that Atma and Atmacites affected pets, this is kind of a let down.