If using Desktop, click HERE
If using Mobile Web (not the app), click HERE
Open the App & log into your account.
Click "Groups I Manage".
Click "Edit Group" next to the group you want to change the group photo in.
Scroll down till you see the "Group Thumbnail Photo" image you currently have and click "Choose File".
Select the photo you want to use from your phone.
Click "Save Changes"
Now that you know how to change your group's background photo, head over to the site and give it a try by clicking HERE.