There is no way to totally remove Link. I think you just don't want to see it on the client screen. Use Settings > Options > Display > then look at what is in the right column under Display. Find Intuit Link, highlight and select the < to make it go away!!
While you are at it, customize other things you might to have on that screen, like phone number, Occupation, Total Fee, etc and add or subtract to get it just right. You can also take those items and rearrange them up or down. Be sure to click OK to save when you are done. You can also do some dragging of columns when you are in the All Clients screen. Have Fun!
This is also a good time to reflect on Settings > Table Editor Spend a bit of time on it to clean up remember mispelings and incomplete Employer or Pension payer data.
You might also want to adjust your fee schedule. Settings > Client Invoice or maybe rewrite a special note in Settings > Client Letter