The question of ownership on this topic isn't as new as you'd think.

If you get a free sports bag from your local training center, is it ethically right for you to use a black marker and erase their printed logo?

I think most people would say that once the training center has given you the sports bag, even if their intention was for you to advertise their brand by walking around with it, it's no longer their property and they cannot control it.

Yes, because most people will not erase their printed logo and they get advertisement. If they notice that most people erase the logo, then they could just stop giving away the bag.

In some ways it's like the adblock debate - and there are JavaScript bitcoin miners (https://news.ycombinator.com/item?id=2566365 ) - uselessly slow now, but the concept still holds.

I've collected a few "ad supported" free items (keychains, bags, writing boards, etc.) from various trade shows and conventions, and of those that are still usable, amusingly enough the logo was the first thing to come off from normal wear and tear.

Have you encountered the new breed of ad-supported free flash drives? I recall from a discussion on HN that apparently some people are putting a hub inside said flash drives and a fake HID device that will occasionally type in "Win+R http://companysite.com <enter>".

No, (un?)fortunately I haven't. I do have a few small ones which I don't use for anything critical, but they show up only as the usual mass-storage devices.

Their hope was for you to advertise for them, they certainly couldn't have counted on it and they know that up front so it's perfectly ethical to cross it out and even they wouldn't disagree.