Pending Suggestions can be removed from withing Donor Central. 
  1. Log into Donor Central
  2. Go to Site Configuration > Admin Portal > Suggestion Admin
  3. Enter a Date Range (required) and the Fund ID of the fund in question. 
  4. Click on the ID Link for the Suggestion that needs to be removed. 
  5. At the bottom of the page, click on the link that says "To Delete this Recommendation, click here".
In DC NXT do the following:

You will need to decline the suggestions in the suggestion import in FIMS and then that will remove them from DC NXT when the next data sync occurs.