Limit New Button on Business Object

Is there a way to limit/remove users ability to click the new button while on a business object, without removing their permissions?

Here is my scenario....

TASK is a supporting business object that does not show up on the New button dropdown by default. However, if you are looking at a task or if you used quick search to look for a task, the new button then becomes 'New Task' and allows them to create a task that has no Parent Type association and isn't tied to a specific parent record.

We want to do different things with tasks depending on what the parent object is (like Incident, Change, CKCS Article, etc...) but if the Parent Type Name is empty or if these have no parent record id association, these tasks just fall through the cracks.