Wrong to be upset about another girl texting my boyfriend good morning?

Anonymous
Recently my boyfriend stayed over at my house after not seeing each other for a week and a half (busy schedules - another problem). In the morning having been up about a half hour still in bed, he was checking his phone (didn't mind that) and sent a text. I asked who it was and he said the name of a girl that has recently started at his work. I asked what he said and he said she said good morning and that he said it back. This bothered me. Over the short time she has work where my boyfriend does (a couple of months) they have become "close friends", text constantly, and he talks about her every time we are together (which isn't often). I felt those texts were inappropriate, they are both in relationships (hers almost just ended) and shouldn't be sending texts like that. She should be texting her own boyfriend good morning, not mine. The bigger part of the issue is that my boyfriend didn't see anything wrong with it and didn't respect my view and feelings about it at all.
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Wrong to be upset about another girl texting my boyfriend good morning?
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