At the temple:Grym gives Callista what any Karlsson sister can...a chance for Kane to live. Callista tells Grym that Kane is the key, which ensures that he's not simply killed right away but given a chance. Then, depending on how we, the players, choose to have him act, Kane may or may not be "worthy" of keeping alive but they still need his sperm. That's the "actual substance" but you can argue in theory that Callista could have approached any sister. Apart from that, we DON'T know Callista's plans since we're NOT Tess...so I'm going to call this conversation over until Tess reveals more in coming updates.
My memory may be hazy but in the temple scene, was it stated the Gambit Queen refuses video communication? I recall she refused to meet in person, and it was just her basically on speaker phone with Grym Guddina in the temple. I don't recall mention of video communication. Grym doesn't seem to know the whole Gambit plan but she does knows more than Jules. We don't know if she knows more than Veronica. Nothing Grym has said suggests she knows the whole Gambit plan to my recollection. The only thing we know that Grym knows about the Gambit Queen is that she is a third party outside of the board. None of what you said is evidence Grym knows who her benefactor is, just who she can eliminate from the list of possibilities. And you said yourself that she doesn't know Calllista...which would suggest that Callista isn't even on Grym's Gambit Queen suspect list...
From what we've been shown by Tess, the only people who know that Callista is alive in the Karlsson group are V, Astrid, Elena, and Kiyomi. Some may like to assume Olivia knew since she was there to witness the "helicopter accident" and she's a good actress. Delilah might not even know considering how Cynthia treats her but I digress. There's no real mention of Alessa's mother but that doesn't mean she was absent. We literally just weren't told anything about their relationship, or lack thereof, to know either way. My point is, again, we haven't been shown anything yet to suggest Grym knows exactly who the Gambit Queen is so she wouldn't be wondering why Callista would support a "non-daughter." She's possibly wondering why this mysterious Gambit Queen is supporting her, but Tess hasn't revealed in game much else to know what and how much Grym Gudinna actually knows or thinks.
G: And of course you're not here in person. More speaker fun.
Meaning this is the typical way they've been communicating. My point being she hasn't seen Callista.
Remember at the pool, Alessandra briefs Kane on what the proverbial "gold medal" he potentially can win in the rehab program, and also slips that if he succeeds he will be worthy of having [at least one of] Alexander's daughter(s), (she uses "daughters" but this probably means "pick of the litter" rather than all of them.) She may not know about the Alexander Jr. objective, but she definitely knows a winning Kane will "join" the sisters. Plus the phone conversation on Day 1 between Dominique and Juliette shows that the whole Board knows that Kane is important, and they all want to know what he's like, so Alessandra would already know not to kill him.
Q: [at the next Board meeting] You will learn what your father truly wanted from the person that will inherit his entire empire...for that, you must turn Master on your direction...you will see that he is the final key.
This sounds like Alexander Jr. was supposed to be revealed at the next Board meeting (where Olivia meets them all, but before she arrived), however Veronica doesn't reveal that part until day after, instructing to keep it from D/J/A/O, and then Callista asks he why she revealed it so early, so something's not adding up. Again Callista tells her to draw Kane to him, with the reason being that he is the FINAL key to inheriting Alexander's empire (aka the Gambit Winner). If Callista didn't think Grymm wants the crown, she wouldn't waste time telling her how to get something she doesn't care about. If she wants Grymm to win, then she put her on the fast track to victory. If she wants to ensure that Grymm doesn't win, either a) she wouldn't say anything, or b) give her bad intel.