Maitimo loves him and - should probably focus on hashing this out, now.
So Maitimo's default move if he gets sent back to Arda is to convince everyone that Telumë is too evil and reckless to trust with the war effort. ("Incidentally, I think that's clearly untrue; if I believed it I'd be all in favor of helping you build your god!") He thinks he could succeed at this; it is the kind of thing he's good at and he knows the people he'd have to convince exceptionally well. Telumë knows this and can't let him, so he can either send Maitimo back under some kind of oath not to do that or he can try to keep this a secret and not send Maitimo back at all. There's sort of an argument that Maitimo ought to push in one of those directions and hope that they blow up in the alliance's face at some point but -
- he doesn't want to. He doesn't really want to be making important strategic decisions with half his head missing at all, really, and he sees a route to getting his head back and he's willing to trade this particular avenue for affecting the world for having his head back. And - and he's watched what it is doing to Telumë to have the path to his goals run so sharply through destroying the person he loves and it does not seem like it's been very good for Telumë's ability to accomplish his goals so he prefers not to put himself in that position.
So he will agree to work with Telumë, cooperatively, under whatever kind of magic verification Telumë wants, for the duration of the negotiations about his release to Noldorin custody, on making sure that this doesn't blow up the alliance. As part of that he thinks they should call in his father, and call in Findekáno, and talk through the question of whether Telumë's judgment is too poor to be running the war effort, without Maitimo deliberately trying to steer that conversation towards 'yes' - "I guess you can decide whether you'd like me to steer it to 'no' or just not steer it, though I kind of think that if you want to add some new checks on your judgment and character you should probably not look for them among important Noldorin political figures most likely to be furious about this, so you should have me steer them to 'no' and then, I dunno, talk with Vanyel? Talk to me, maybe, while I'm modeling the person you fell in love with - anyway, once I have presented the situation to them in a reasonable way and they've decided how mad they are with you, and we've explained why I'd try to use this to break the alliance and they've decided whether they endorse being manipulated into that, that stops being a good avenue for me to interfere with the war effort once I return to Valinor, and I will have to occupy myself some other way."
And in exchange he wants his head back, entirely, insofar as that's a meaningful concept when they both know that his head is almost entirely sculpted around Sauron.