Following steps can help us to stop receiving updates from Quark,

Solution 1:

  1. Quit QuarkXPress.
  2. Navigate to:
    Mac OS : Mac HDD>Applications>QuarkXPress 10>XTensions>
    Win OS :Local C: Drive\Program Files (x86)\Quark\QuarkXPress\XTensions\
  3. Move the XTension named 'AutoUpdate.xnt' to XTensions disabled folder.

Solution 2:

  1. Launch QuarkXPress.
  2. Navigate to:
    Mac OS : QuarkXPress >Quark update settings>
    Win OS : Help> Quark update settings>
  3. Select Manually.
  4. Click OK.