So, to do this you will need to be in the trip trade page. In the upper left you will have 2 arrows, not the clock. In the left pane (Duties) you choose the trip you want to remove legs on, then after it expands select the legs you want to drop.
Select the button that is near the title duties that says "Create Offer One to none) as you hover over it and select it-- it is two small arrows. It will put on the Available offers. If you want to trade it for something else, choose "Create offer in trade pool" and if you want to send it to an individual, you select the last one which has the arrows with the outline of a person.
It won't be removed from your schedule until someone grabs it.
Mustang304