Which term refers to modifying, delaying, or disposing of the main motion?

The term that refers to modifying, delaying, or disposing of the main motion is indeed "subsidiary." In parliamentary procedure, subsidiary motions are specifically designed to affect the handling of the main motion. These motions allow members to suggest changes to the main motion, postpone its consideration to a later time, or even dispose of it altogether.

For instance, a member might call for an amendment, which modifies the main motion; another member could propose to table the motion, delaying any action on it; or they might seek to reconsider it at a future meeting. All these actions fall under the category of subsidiary motions, which are used to manage the discussion and progression of the main motion effectively.

Privileged motions, while important, are primarily concerned with urgent matters that take precedence over the main motion, such as requests for a recess or the setting of the agenda. Incidental motions deal with issues that arise out of the procedure concerning the main motion and related business but are not primarily focused on modifying or disposing of the main motion. Lastly, the main motion is the primary proposal that the group is considering, and thus does not fit into the category of modifying or dealing with itself.