How do I removed or prevent green box icon on Garmin after importing from Basecamp?

It's a pin, unfortunately your device along with all DS devices doesn't support custom icons so it is what it is. You can perhaps limit them by changing any viapoints to shaping points.

Do you mean waypoint not viapoints. Because it that is what you mean none of these green icons are waypoints they are waypoints. All my waypoints are orange flags. 

Sorry I meant all the green icons are shape points not waypoints. All my waypoints are a orange or red flag. 

Your terminology is confusing. Viapoints are points on a route that are announced. Shaping points are points on a route that aren't announced. Your device will insist you visit any viapoint unless you take action to skip it whereas you can easily bypass shaping points.

If those green pins are shaping points then your DS works differently to the DS versions that I have, my shaping points just appear as small blue dots, and I can see no way for you to change them, but you do have an awful lot of them, are they all necessary?

I rarely need more than a few viapoints and shaping points on routes, even ones of hundreds of miles, so perhaps look at how you're creating routes as you shouldn't need the number of points shown in your screenshot.

Incidentally your screenshot also shows the normal symbol for shaping points, so are you really sure those pins are shaping points and not favourites or waypoints that are showing?

I can't speak for you device, but when BaseCamp sends a route that contains waypoints (regardless of the via or shaping setting) it also sends the waypoints as separate objects (i.e. it is the same as sending both the route and the waypoints).  The only way to avoid this is to replace the waypoints with a point created by clicking on the the map using the route editing tool.