Conoco may not be able to do a whole lot.
Generally a station will either be company owned or branded. The company owned station (usually the larger, open 24/7, high volume, mini-mart/car wash, carry all fuel grades and diesel) is usually leased to the operator. They cant do much until the lease expires, usually.
If its a branded station (usually the smaller, non-24/7, mom/pop type stations) about the only thing they can do is pull the signs. Theyd probably have to wait until the contract expired to do that too.