Here is how you can hide the number of registrations available for each participation type.
  1. Select Fundraising > TeamRaiser 
  2. Click "Edit" in the action column next to the TeamRaiser
  3. Click "Manage Participation Types"
  4. Click "Edit" in the action column next to the participation type you have limited
  5. Click "Select Type Options"
  6. Find "Remaining Registration Slots Hidden from Participants"
  7. Mark the box for "Do not display the number of remaining slots on registration pages"
  8. Click "Next"