It all depends on how the phones are checking for Internet connectivity.
If the phone is trying to connect to a specific Internet website or IP address to determine if it's conencted to the Internet then, no, there is no easy way to resolve the problem.
The other thing that might be happening depends on your setup. Do the DHCP clients (the phones) get given a gateway IP address (even if it isn't a real gateway)? Some systems, if they don't have a gateway IP defined, assume that the network is down and will disconnect. The simple solution in that case is to put in a gateway IP that can't route traffic (or blocks all traffic going to the Internet).
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Backups are your friend. Always make a backup!
/system backup save encryption=aes-sha256 name=MyBackup
Please, export and attach your current config to your post if you want help with a config issue:
RouterOS v6 code
/export hide-sensitive file=MyConfig
RouterOS v7 code
/export file=MyConfig