Postdoc application, different team, same institute
If you're interested in the new position, just go ahead and apply! If the two teams in question are working in closely related fields, the new position is presumably a good fit for your profile anyway. In that case you're unlikely to look like someone who just wants to work at that institute. If they're in rather different fields (maybe they fall on different ends of your spectrum of interests) make sure you really explain why you're interested in the cover letter.

In any case, what's the worst that can happen if you're viewed as only looking to get into institution X? You don't get the position there? Well, you're even less likely to get it if you don't apply for it...