Ser Davos' text read:

Response: Kneel Ser Davos Seaworth to save an atttachment on a character from being discarded from play. Then, attach it to another eligible character, if able.

Is this to save any attachment, controlled by any player?

If so, do you take control of the attachment?

Someone treatened to discard one of my attachments, then use Ser Davos to take control of that attachment ….

Seems a bit powerful for little cost and I would have thought that the text would say take control

Maybe you can still save and re-attach an attachment contolled by an opponent, but then that opponent retains control of it?

I can't work this one out without seemingly having to make some assumptions

HastAttack said:

if it does not specifically say to take control of something, it means it stays in control of whatever player currently controls it. I don't see why you couldn't save one of your opponent's attachments if that's the exact wording on the card (on a phone, so can't effectively look it up)… Like Flame Kissed, Dragon Skull, Bastard, Mötley, etc. they would still control the attachment, but you get to choose its new target.

HastAttack said:

Is this to save any attachment, controlled by any player?

Yes.

If so, do you take control of the attachment?

No

Maybe you can still save and re-attach an attachment contolled by an opponent, but then that opponent retains control of it?

Correct.

As an added FYI, Davos allows you to save attachments from characters that are dying. The attachment is being discarded from play (even though it is "normal") and as such you have an opportunity to save it and relocate it.