There have been threads on this before, so I'll just copy/paste one of my previous responses.:
You may want to look in to the XS rear sights. Check these out:
http://www.brownells.com/rifle-parts/sights/sight-accessories/replacement-apertures-prod26047.aspx?avs|Manufacturer_1=XS%20SIGHT%20SYSTEMS
The post replaces the factory post on your GSR. The .150 post is just that, a simple .150 diameter aperture post. The .218 diameter post, however, is threaded on the inside, and you can screw in a Williams Sights aperture. Here are the apertures:
http://www.brownells.com/rifle-parts/sights/sight-accessories/sight-apertures-prod862.aspx.
You can also use the Williams Sights Twilight Apertures found here:
http://www.brownells.com/rifle-parts/sights/sight-accessories/twilight-apertures-prod26077.aspx.
As you can see, the apertures can get down to .050 and up to .125. That gives you a couple more options to play with, and at ~$10 per piece, you can have a new rear sight and aperture on factory mounting for as low as $20. All of the Williams Sights apertures I've listed are threaded for the same pitch, and will fit the XS post.
Two caveats: First, you may have to modify some of the real estate on the back of the sight, just behind the sight post, to make room for the Williams apertures. Your particular rifle may require this, I can't say for sure because every rifle/ammo/shooter combination is different. On my personal rifle, I did not have to do any modification, it was a simple bolt-on piece. Second, at some point in production Remington changed the threading on the rear sight post to a newer piece. The post screws through the base and in to a small "slide," which is a flat piece of metal with the threading for the post. This fits under the base, and is what you loosen when you adjust for windage. If you have a newer GSR, you will probably need one of these replacement slides to fit the XS post. This new slide can only be ordered via telephone from XS sights. You can call them at 1-888-744-4880, M-F 9a-5p CST using part # 23-2004A-100-1.
YMMV, but now you're aware. For the record, the factory aperture on the GSR is approximately .105.
Here is the original thread over on scoutrifle.org about the apertures:
http://www.scoutrifle.org/index.php?action=printpage;topic=2699.0
Here is my GSR with the 0.092" twilight aperture. This is my standard go-to aperture.
Here it is with the 0.050" twilight aperture. This one is VERY small, not good for close-up snap shots, but much easier for 400 yard steel plate shots. I keep this in my pocket when hunting, but I haven't had the need to change it out in the field just yet.