Stalking ex...is that an issue?

have a new gf and as soon as her ex found out he starts texting her, appears at her work and tries to talk to her...she says don't pay attention to that but when he writes she says she replies and then nothing else but it's startint to piss me off...do i have grounds for this or just let it go..she says she loves me and wants to be with me, she has forgotten her ex