Break it off or no?

My boyfriend and I have been going strong for 3 months now. We’ve had our ups and downs but remained together and communicated to work things out. We works as a waiter and a local restaurant and tries to get more tips by inviting people in. He told his girl that he was single and she already knew he had a girlfriend. She messaged me showing screenshots of their messages. I confronted him about it and he told he he did it to get more people in. I’m confused. And need help. No physical actions were involved. So should I break it off or no?