Remove monitoring of server from recovery site.

If the two BigIP's are in an HA group, you would need to manually remove monitoring each time you synced. If they are not in an HA group, it would be simple enough to remove the monitor from the pool member on the DR site. I am assuming that the server is intentionally not visible to the DR site.

To remove monitoring go to Local Traffic, Pools, pick the pool, select members, go to the member, select Advanced under Configuration, and set health monitor to None.

As noted, when you sync, if this is the HA peer to the main BigIP you will need to repeat this. It shouldn't cause any problems to leave it be, however.