Jellicle Melody Has Been Declawed

Apparently my husband and Jellicle Melody (not "officially" our cat, because Gary fussed at me for giving it milk at Christmas although he turned around and fed it night after night and then we decided to name it and started petting it and Gary has now bought specific cat provisions at the store for it because it was destined to chip its tiny teeth on the big dog food) have been having late night tete-et-tetes in the hot tub. I know - pretty scary, but let me further explain. The cat, who we think is a girl but are still not 100% certain, walks around the edge of the hot tub, and settles in on the head rest, right next to Gary's head. Last night, they apparently were "playing," and the cat was pawing him. Gary said that she has been declawed - a rather expensive procedure for cats. "This was somebody's cat!" he exclaimed. Now we don't know what to do. The cat came to us with no collar, however Jake has wandered out without his collar, too, after receiving a bath. Should we post flyers? Should we leave well alone? We have taken a fairly firm stance that the cat is not coming in the house - it's much better as an outside cat for many reasons. However, Jake, also, has taken to the cat. At one point in the entire affair, Gary had the bright idea to take Jake to the door, and "scare" the cat away. Of course, the exact opposite thing happened - they became instant friends.