She didn't tell him anything to convince him. She simply intimidated him, and he did not do anything while she released the droid.
But earlier, she told him to halt what he was doing:
At least until she understood the particulars of the confrontation she was witnessing, it was only right to call it to a momentary halt.
Motion ceased as both the Teedo and BB-8 stopped wrestling and turned to peer up at her.
“Parqual! Zatana tappan-aboo!”
Making an effort to simultaneously control both its heavy-headed mount and its captive, the Teedo yelled back through the mouthpiece of the goggle-eyed helmet that covered its reptilian cranium. Its attitude was decidedly unconciliatory, even threatening. Meanwhile the hovering head of the imprisoned droid swiveled rapidly back and forth, trying to watch both Teedo and human simultaneously.
Rey immediately took offense, not only at the Teedo’s tone, but at its speech, which far exceeded the bounds of common courtesy that existed between fellow desert-dwellers and made difficult coexistence possible. The luggabeast rider knew better, and its intemperate words were enough to decide her on a course of action. Descending the far side of the dune, she drew her knife and began hacking at the netting.
“Namago!” she growled. “Ta bana contoqual!”
Observing that it was on the verge of losing its prize, the Teedo unleashed a stream of indigenous invective. None of it had the slightest effect on Rey, who continued cutting away at the mesh until the native promulgated a slur that would have been vile in any language. Pausing in her work, she turned to face the tightly clothed creature, gesturing with her knife and fairly spitting a reply.
“Noma. Ano tamata, zatana.”
Long and drawn out, the Teedo’s response to this would have been unprintable on any of a hundred civilized worlds. Turning the metal-enclosed head of its mount, the unpleasant scavenger departed in the opposite direction. As soon as the native was a safe distance away, BB-8 rolled clear of the netting and began beeping loudly and challengingly in its direction.
“Shhh,” Rey hastened to quiet the droid. “Don’t tempt it. Enough insults can override anyone’s common sense, even a Teedo’s.” BB-8 instantly went silent. Together, the two of them tracked the luggabeast until it and its rider had vanished from view.
An electronic query drew her attention. Rey knelt down beside the questioning droid.
“He’s just a Teedo. A local. Not so unlike me, really.” Her expression twisted. “Except this one was particularly impolite. Wanted you for parts.”
Since we don't have a translation, we can only guess at the exact meaning, but one can PROBABLY guess it was something like "this isn't salvage, leave it alone".