@Commodore50 I highly suspect BT won't be at all bothered about losing you as a customer, it's par for the course in the ISP world, so don't fret over that, although, see the later part of my post.
From your own enquiries, it seems there is little will to help you and whilst it's appreciated that you're preference is to move to EE, you'd just be moving internally within the BT Group, so of course they will I suspect have little interest in resolving the Telecare Flag. Whether or not that would be same if you switched to Plusnet, I have no idea, but it might be worth giving them a call if you don't need a phone line.
If it were me and you actually wanted to stay with BT or move to the EE product, one way of resolving the issue might be to initiate a switch using One Touch Switching to a non BT Group ISP. What will happen then is that BT I can literally guarantee, will start calling you, your phone will be lighting up like a Christmas tree because bizarrely, all of a sudden, they don't want to lose your custom. Then you can tell them straight about the Telecare flag and tell them you'll move ISP unless they take the marker off. It might work, it might not. The problem is, the Customer Sales team are there specifically for one thing, to sell the product so they might not actually have the know how or even be bothered to contact the right team to take the marker off.
If you move ISP, I can only surmise that the Telecare flag will be removed as part of the switch, though of course I have no experience or proof that is what would happen.
It would be nice to see if a Moderator could assist.
