I would, but I can't get InDesign to produce that kind of object. When I paste, it's a path.
Please show us the layers panel.
I found the solution:
Freehand paths and shapes pasted into InDesign, some of them filled with text in InDesign:

It seems that the key was my clipboard handling settings and that I needed to ignore text wrap for the text frame when it was selected with the directs election tool in InDesign, and the text shape was brought over as a shape with fill not as a text shape, I made it a text shape in InDesign by clicking it with the text tool, I don't remember how I removed the fill of it. But I could remove it.