Someone left a towel off to the side of a green. Two questions: What if the ball had come to rest in/on the towel? What if the ball kicked off the towel into the nearby hazard?
If the towel has been left by a previous group that is not in the same competition, the towel is a movable obstruction. Free relief if the ball comes to rest on or in the towel. If it kicks into the hazard, it would be the same as kicking off a rake or movable hazard stake or an empty beer can…got to play it where it lies.
If it is from one of the players in your foursome, it is “equipment”. Rule 19 applies. If the towel belongs to you or your partner, or your caddie or your partner’s caddie (in stroke play and match play), there is a penalty stroke and the ball is played where it lies unless it is in or on the towel and then the ball is dropped. If the towel is on the green, the ball is placed.
If the towel belongs to a fellow competitor (in stroke play), the ball must be played as it lies with no penalty. If it comes to rest in or on the towel, the ball is dropped (or placed on the green) with no penalty.
In match play: If the ball is stopped or deflected by your opponents towel, you may choose to cancel the stroke or play the ball where it lies with the same free relief options if it comes to rest on the towel.
This situation happens a lot. With clubs, putter covers, and towels being brought to the green by most of the foursome on every hole, the odds of this situation is great. Occasionally a putt is hit too hard and is headed for another player’s equipment. This equipment can be picked up. There is a myth that you cannot move any objects while a ball is in motion. Equipment can always be picked up. The flagstick is not equipment. Therefore, if someone’s ball is headed for the flagstick, too bad. Penalty strokes are coming. Same if the ball is headed for a towel that belongs to the player that just stroked the ball…penalty strokes are involved and you need to let that happen (unless the equipment is your partner’s and then you can pick it up).