I would not waste time with a little TM571 antenna. I just finished replacing my little plastic CM15A antenna with a telescoping one from Radio Shack with excellent results! It took only 2 minutes.
Here's the Radio Shack part number 270-1402 Replacement 34 3/8" Telescoping Antenna for $4.99. You don't even need to open your CM15A to install this new antenna either. Just grab the middle of the existing plastic antenna with a pair of pliers and pull upward. The plastic housing will slide up and off. It's made that cheaply. Leave the elbow joint attached to the CM15A, as you're just pulling the vertical antenna plastic off. You'll find a little gray wire inside, just hanging loose within the plastic tube. You want to strip off the end of the gray wire's insulation (about one inch). Then wrap the bare wire around the threaded hole in the base of the replacement metal antenna. Do two wraps. The replacement antenna comes with a screw which is too small to fill up the hole, but since you've wrapped the bare wire through the hole a couple times, the screw will thread into the hole and lock there, using the wire strands for filler. Next step: hold the metal antenna against the side of the CM15A case. Run a couple lengths of black tape all the way around the case of the CM15A to hold the antenna up. Extend the antenna all the way up. If you have extra gray wire hanging down from the bottom of the antenna screw, just push it back into the CM15A case hole. Plug CM15A back in somewhere.
My range tests with KR22A 4 Unit Credit Card Controller:
before mod, plastic antenna = only 12 feet in the clear, only 6 feet through 1 wall
after mod, metal Radio Shack antenna = 50 feet through 3 walls