I tried to force it to zero by script, but it didn’t work.
Although this is just a small number, my movement code needs an precise value (zero velocity if not moving).
How to fix this?
Unfortunately, I don’t know in which coruse and lecture you are but 1.5e^{-5} is 0.000015, which is basically 0 in Unity. Since the physics simulation works on all Rigidbody components (e.g. because of the gravity), it is normal that the linear velocity is basically 0. See, for example, this discussion.
When not moving, you could try to force the Rigidbody to sleep if you do not expect any collisions with moving objects.