You'll need to connect it to your computer using the USB cable and enter into Mass Storage Mode. Then browse to the X:\GARMIN\GPX folder (Where X: is the drive letter assigned to your garmin unit when plugged into your computer).
In the GPX folder you'll see all the GPX files for the caches you've loaded. I'd recommend copying them to your computer as a backup first. Then start removing the ones you no longer need.
It sounds like you are sending individual caches over in GPX format. Using Pocket Queries will allow you to have more caches stored in fewer GPX files. I think there's still a 2000 cache limit (or is it 2500). However a single Pocket Query query can contain up to 500 caches based on your search criteria (or more if you use GSAK to create your GPX).
This sounds really simple....but when I connect it to my computer using the UBS cable...how do I enter into Mass Storage Mode???