Yeah, there's, definitely some potential problems that could arise from going off on our own without our sworn shield, even aside from any actual threat to our safety. Going off alone with Gwayne or Steffon could raise concerns about our chastity if anyone dared to raise them, since we wouldn't have a chaperone. Rhea's, *probably* safer from that sort of rumor mongering, but there's probably still some whispers that have been emboldened by us crowning Alicent to make some comments. Probably less of an issue than the other two admittedly. And then we're just, in Winterfell and then the wall without an actual escort? Hm.
I doubt it'll be a significant issue, and it doesn't look like anyone really wants to force Tarly to come along, but it's probably gonna be another avenue for people we've pissed off to spread rumors.