I read the Hunger Games books a long time ago so maybe there's an answer there that I don't remember, but from the movies Haymitch makes it seem like Peeta couldn't be rescued from the arena because his tracker was still in his arm. Why couldn't they have simply cut it out of his arm in the hovercraft on the way to District 13? Then they could have easily disposed of or destroyed it.
Furthermore, it seems they could have done this for all the rescued tributes. Removing the tracker on board seems like it would be far less painful (since they seem to have anaesthetic on board), more sanitary, and wouldn't have given the capital a moment to react when they saw the trackers being removed in the arena during the games.