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The little green worms probably are sawfly larvae, commonly called rose slugs. There are two different kinds and the life cycle of one begins in late summer and is currently in full swing.
If you Google "rose slugs" or "sawfly larvae," you'll find a wealth of information about these creatures and the damage they do. The safest way of controlling them is with a spray of water. Like aphids, rose slugs are not attached firmly to leaves, will be dislodged by a spray of water, and can't climb back up the plant. Various pest control methods will also work, but not the one commonly used for caterpillar control (Bacillus thuringiensis or Bt) because these pests may look like tiny caterpillars, but they aren't related to caterpillars in any way.