Posting here. Roku implemented this for third party apps to gather information on what is watched to bring users back to the third party app. Google "continue watching Roku developers". To get rid of it, I did the following and it worked:
1. Press * for Options on each show in continue watching and select hide or remove (don't recall word used).
2. Press * for Options on the Add Channels and Sleep Timer icons on Home Screen and remove. This removes all shortcuts on Home Screen, which Continue Watching fell under.
3. Go into Settings-Home screen and hide What to Watch, Featured Free and Shortcuts.
4. I also removed the Roku channel icon, pressed * for Options on the ad to right of Home Screen and selected hide, reset advertising identifier under Settings-Privacy-Advertising and deselected Personalized Ads and Smart TV Experience, and logged in to the actual website of each third party app through a computer deselected sharing of information with third parties. Not sure all of this was necessary, but Roku obligates the the third parties to obtain a user's consent to show the Continue Watching on Roku.