Hello Honda750,
I understand that you are trying to delete the ad group out of the list on the left naviagtion bar in the adCenter Desktop.
You are correct. If you right click and then click delete it will put a Strike through the ad group that you delete.
After that if you press "upload changes". It should reflect in the web interface if you deleted the Ad Group.
You will then just have to download the recent changes back into the adCenter Desktop and that ad group will disappear out of the list.
If you have any other questions please feel free to reply to this post.
Thank you,
MS adCenter Support