Your ball is resting beside a tiny twig and your playing partner acts like it's a protected historical landmark. Here's the actual rule.
What is a loose impediment?
A loose impediment is an unattached natural object such as a leaf, twig, loose stone, or pine cone. Under Rule 15.1, you can generally remove loose impediments anywhere on or off the course.
What if the ball moves?
Outside the putting green or teeing area, if moving a loose impediment causes your ball to move, you generally get one penalty stroke and must replace the ball. On the putting green, there's no penalty for accidentally moving your ball while removing a loose impediment, but the ball must be replaced.
Don't confuse it with an obstruction
A cart path, sprinkler head, or other artificial object is not a loose impediment. Different rules apply to movable and immovable obstructions.
Fore Alarm takeaway: Learn the rules, embrace the chaos, and enjoy the round. Golf is serious. We're not.
Official rule reference: Rules of Golf.
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