QWithin the teeing ground, I know that there's a Rule that allows me to pluck grass or press down on the soil with my foot to create a certain lie. However, if a small branch from a nearby tree interferes with my swing, may I break it? - Barney (Pawleys Island)
ABarney, because the answer is no, you'll need to leave that tree alone.
You alluded to Rule 13-2 "Ball Played as it Lies; Improving Lie, Area of Intended Stance or Swing, or Line of Play" that allows you to create or eliminate irregularities of the surface within the teeing ground or remove dew, frost, or water from the teeing ground. Focus on the word "surface." Since the tree to which you mean such harm does not exist on the "surface" of the teeing ground, you cannot break the branch and improve the area of your intended swing.
Decision 13-2/14 discusses this exact situation. If you broke the branch, you'd either lose the hole in match play or receive a two-stroke penalty in stroke play. The penalty would be the same even if you broke the branch and, before playing the stroke, re-teed elsewhere on the teeing ground - see Decision 13-2/24.
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So, all this means that you'll need to either deal with the interference or simply move to a different spot within the teeing ground. Then, simply mention the problem to the course staff later.