How am I supposed to deal with this?

My boyfriend has a four year dog, he bought this dog when he was with his ex and after they broke up, my boyfriend kept the dog but he also kept the contact with his ex.. He always mentions that this dog is 50% him and 50% his ex and that the relationship between him and his ex will forever maintain because they have a dog in between.. I don’t like the fact that they talk continuously and that they spend some time the three of them.
What you guys think about this story?
How am I supposed to deal with this?
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