There is no "removal" requirement written in the National Electric Code. However, if in the course of work on, or care of, an existing dwelling with K&T installed, if one insulates or reinsulates in the area of the existing K&T one cannot put insulation in contact with the K&T. Replacing the existing K&T with a modern wiring method is almost always the easiest way to get a good insulation installation.
I work in an area that has a history of local ordinance that requires existing electrical installations to be "maintained" by certain improvements that would be enforced, most commonly, when a service size change occurred and the local jurisdiction had the leverage of denying the permanent electrical connection from the local Power Company.
Some insurance companies claim that K&T must be removed from service if they are to issue an insurance policy on the property. They do not have the force of "Code" but do play on a customer's loyalty to an insurance company, and play on fear of electricity.
So, the answer to your question is not simple and requires knowing local ordinances, if any, and requires an understanding of your customer's insurance.