As far as I know, GarageBand doesn't add anything to the end of exported tracks, but it exports as much as there's sound in any track. Therefore, to avoid having extra "stuff" exported, you should always create a loop region and export with that. As you can see in the following picture, I'm at second 47 in the "timeline", however, I've created a region (the yellow bar on top) that starts at second 1 instead of 0, therefore creating a 46 second clip.
The exported version can be seen in quicktime with a length of 46 seconds, without any extra silence or sound.
In order to create such region, you have to activate the "repeat/loop" (next to the Play button in GarageBand). That will create an extra space below the Beat Bar (where you move the Play Head). When you hover your mouse over that small region, the cursor changes. You can click and "drag" to paint the yellow zone. That's the zone that will be repeated over and over.
Always export with a repeat/loop zone created and Garageband will only export that.
NOTE: Logic Pro/Express behaves the same way when creating bounces.
There's a draggable cursor at the end of the timeline on the upper right corner. If it is beyond the end of your sound on your longest track GB will include that much silence. Drag it back to the end of your longest track, or leave however many seconds of silence you want.
Update 2020 - What about iOS?
I don't use macOS anymore but if you want to do this on iOS or iPadOS, if I don't incorrectly recall, your only choice is to have a region that encompasses the part you want to export, tap it (to select it), then tap it again (to see a floating set of buttons), and pick "Loop". I don't know/think there's a way to do the same "playback region selector" on iOS. I may be wrong, but this question was about the OS X version of GarageBand so I don't know more :)
My Setup: Crashplan, OS X 10.8.2, iTunes 10.7 (21)
I am unable to replicate the same issue on my system, and haven't noticed any excess changes or uploads to crashplan on my filesystem after playing music. To be sure it wasn't happening in the background, I ran a checksum on one of my audio files, played the complete song in iTunes, and re-ran the checksum. If something in the file itself had changed, the checksum would be different.
Here are the results:
Big-iMac:Abbey Road dave$ openssl sha1 17\ Her\ Majesty.m4a
SHA1(17 Her Majesty.m4a)= 3aea5150d7b1d21846b6502bac7ccacca44ff0fa
Big-iMac:Abbey Road dave$ openssl sha1 17\ Her\ Majesty.m4a
SHA1(17 Her Majesty.m4a)= 3aea5150d7b1d21846b6502bac7ccacca44ff0fa
As you can see, the checksum matches the second time after playing the song through iTunes. Most of my collection is ripped into ALAC (m4a), so I thought I'd test a standard mp3 file as well:
Big-iMac:One More Night in New York City dave$ openssl sha1 2-21\ The\ End.mp3
SHA1(2-21 The End.mp3)= a223d6fb542bee5191794d0a74f971da19fb9afc
Big-iMac:One More Night in New York City dave$ openssl sha1 2-21\ The\ End.mp3
SHA1(2-21 The End.mp3)= a223d6fb542bee5191794d0a74f971da19fb9afc
This too produced the same checksum before and after playing the song in iTunes. All of the metadata about your library (play count, etc.) is stored in the iTunes Music Library.xml file, not in the mp3 itself so I wouldn't expect individual songs to change. However, it's quite possible that the iTunes Music Library file will need to be re-uploaded since it changes frequently.
Best Answer
I suspect this is not a file compression issue but rather an audio compression issue. By default, GarageBand has "Auto Normalize" turned on (Preferences > Advanced). This reduces the volume difference between the softest and loudest sounds in the mix on export, so that the playback of the finished audio is louder. The problem is, when you've got quiet background noise in your source files, normalizing will make it louder. Try turning off "Auto Normalize" and exporting again. The file format shouldn't matter.
Of course, the Jedi master-level fix for this problem would be to get a better recording (or better recording equipment) and to EQ/filter out the noise while mixing!