For my total conversion I need to get rid of those pesky Travel Markers. If I want to delete them it says I can't "If you want to get rid of this remove the travel service on the owner". I don't understand this. Is this about the NPCs? I checked all my NPCs (only got 20 so far) and NONE of them have Travel Service enabled.

So again my question: How to remove those Travel Markers?

Just like with doors, you can't delete the marker itself. You have to delete the door it's connected to.
So, for your problem, you need to find the NPC that Travels you to that marker, then remove the travel service from the NPC. Or delete the NPC from the Object Window (just deleting the NPC from the world won't be enough)

I am sorry, this didn't work out. I've deleted all NPC's from the game, so there's only the player left in the object window. Still, I got 53 green Travel Markers in the outside world. Could it be they are linked to some other objects instead of NPCs? And if so how do I find out to which objects?

Green Markers are linked through NPCs.
Removing the Travel service they offer (it's under the AI tab in their reference window) will delete the arrows.

Did you know that there already exist almost blank Morrowind ESPs, so that you don't have to delete everything yourself.

Yes, but they all seem to be ones without Bloodmoon, and most without Tribunal.

I am also working on an esp with just the land and leaving interior cells intact. I want all the things available, including Tribunal scripting and Bloodmoon changes as well.

What blank esps are there now that include the Tribunal and Bloodmoon assets?