I think the issue would be to veto or kill the petition to Target to NOT allow CCW carriers.
Target doesn't have a policy on the issue. If they see your gun and feel uncomfortable about it, the store manager can ask you to leave, like in any other nonposted business. Same as WalMart.
I feel like sending a preemptive petition to allow it (when they've not denied carry) is asking for trouble and attention where it doesn't necessarily need to be.