Exclude Local IP for DNS on VPN

Haven't been able to find an answer on this, but is there a way to block a machines local IP address from updating DNS when they register? The private DHCP pool we give them on F5 is in the 10.x.x.x/23 subnet and need DNS to get updated for that, however, I want to block their local IP from registering on our DNS.

We use Infoblox here for DNS. I thought about blocking some of the subnets we don't want it registered, but that is a management nightmare and rather just block it on F5. Below is a screenshot of the DNS settings. I wasn't sure if unchecking the register part would mess up the IP given by F5 from registering.