GTM design question: GTM/LTM LTM/ASM multisite deployment iquery requirements

in a traditionnal GTM design, all GTM should have access to all Big-IP it is monitoring. Otherwise in your example if GTM2 cluster fail, GTM1 won't be able to touch you remote devices and they will be seen as down.

Having said that, in your topology, i won't do monitoring by GTM of you LTM/ASM pairs. I would only include LTM services hosted on GTM/LTM to be monitored in the GTM group. As the LTM services hosted on your LTM/GTM will monitor second LTM/ASM level it should be enough.