My friends and I like to play an alternate "best two out of three" gamemode which requires this third goal piece. Here are the rules:

Start the game with this piece in the middle column of the board taking up the third and fourth space from the top. In order to win, you need to "take" two of the three goals. You take a goal by being the first player to get a ball into that goal. Only one player can take each goal, so leave the ball in to mark that the goal is no longer active. Once the upper goal is taken, remove it from the board. (Note that this new upper goal is considered part of the board, not a tile. So effects that destroy, rotate, move, or otherwise affect or care about tiles do not affect or care about this.)

We came up with this gamemode because we found the early part of the game to be a bit too distant from any particular in-game objective. When you're placing your first few tiles, you can't make any actual strategic decisions because it's impossible to determine whether any given play will benefit you or your opponent. It will be a dozen more turns until you start to get close to the end goals. So this makes the early game matter a lot more. If you like the strategic aspect of Hextraction, give this a try.