Is this only with your DVR? Or does it show the green line with ALL sources (DVD players, Blu-ray, videogames, etc.)
If it is just with your DVR, what you are seeing is the "garbage" information that most cable channels store on the very edges of the signal. When you put the V10 in THX mode, it automatically engages the 1:1 pixel mode. In this mode, you get exactly 1920 x 1080 pixel-for-pixel resolution of the source. All of the other modes and the component video input default to an "overscan" mode, where the image is "zoomed" so that some of the edges of the signal are cut out of frame.
You can actually change this setting manually. You set the picture aspect mode to "Full" and then go into the Advanced Picture controls and set the "HD Size" to "Size 2". That will engage the exact 1:1 mode. If you set the HD Size to Size 1, it will engage overscan and "zoom" the image a little bit so that the edges are "cut off"
In THX Picture mode, the HD Size is set to "THX", which is the same as "Size 2" and you cannot change it. So you will get perfect 1:1 pixel display of 1920 x 1080 sources (which is what you want for Blu-ray or upscaled DVDs), but with HDTV from your DVR, you might want to switch to Size 1 HD Size mode so that you get the overscan and eliminate that "garbage" information on the extreme edges of the signal.
Let me know if that helps!