Every message from the L2_CrossDomainMessenger will be attempted to be relayed by the default relayer. Though the attempt to relay messages meant for the Alt_L1_Messenger will ultimately fail, the relayer might still bear the cost of the failed tx. Some ways to remove this -
a. Modify the existing default relayer service to skip attempting relay messages( though they fail internally) when the target is the specified to be the Liquidity Pool
(or)
b. (better) Have unique relayer actor set for the L1_Messenger, who only will be able to call relay method. The default relayer service won't attempt because these tx would fail on the dry run from the very beginning
c. similar to b. instead of having unique relayer, disallow relays from the default relayer address