I mean, it's the Rocks pirates who have to prove themselves, right? Garp came the moment he heard Roger is on his way, that's the only rival Garp cared about and Garp as a Marine basically has enemies in both the Roger and Rocks pirates. Meaning Roger, Rayleigh, Gaban & co. on one hand, Xebec, Whitebeard, Shiki, Linlin and Kaido on the other hand. At this point Garp's disinterest in following pirates that flee anyways is justifed.