I have no evidence that they are, in fact, stealing the property of the American people at the White House. This is really something that is probably being looked at by the people who run things at the facility. There are clear rules for what is, and what is not, the property of the Trump family and what belongs to the government.
All of the furnishings in the White House go back into a sort of warehouse or pool of available items and then the new president chooses what he wants to have on display. It's more of a museum situation where much of the permanent collection is in storage and only a limited number of items are put out for exhibition. There are customary items that are displayed in the Oval Office but who knows what Biden will decide to put in there.
I think the yellow rug has to go. I don't care about the "Resolute" desk. The president actually works in an office nearby and the Oval is used more for ceremonies. But, again, that's up to whoever is president. Trump probably did more to defile and disgrace the place than anyone else. I would not want to occupy it so soon after his departure.
In any event, the Trump family did bring their things and they did receive gifts. They appropriated items from the French Embassy and who knows what else? They have small, light fingers, in other words. The thing is, I do suspect that the lines are blurred because the Trump family has behaved as if everything in the White House belongs to them.
Everything you see could very well be innocent, but it's a bad look to be seen packing up when you never even congratulated the person who won.