"There have been some threads discussing this issue, from the online tree perspective."
I appreciate the responses.
The statement above got me to thinking so I conducted a little experiment. I went to my AMT tree and ignored the hint there. I gave it a while to percolate through Ancestry's system then I sync'd my FTM tree. The hint is gone. Problem solved. I realize it's a somewhat cumbersome method but at least I can get rid of that type of hint now.