All it took for Gwen to trust Carth Onasi was to know that he was a Republic soldier.
She learned soon after that it would take a lot more for him to trust her.
She walked in with a meter of steel in each hand and looked like she knew how to use it. He feared her then, but as she tossed and turned in the clammy sheets in their stolen apartment on Taris, that emotion faded and she was just another soldier, someone he needed to inject with meds every few hours and try to get some water down her throat. Between caring for her and maintaining his own health and weapons, he wondered how long it would take for security forces to find them and why the city has fallen this far, or whether every city has abandoned housing towers.
When she recovered he learned that she walked without much sway in her step, woke up and cleaned up fast, didn't ask many questions.
He trusted her blades before he trusted anything else about her, and so did she, and for a while that and soldiery were the only things they had in common. Those two things were enough.