You don't say how you plan to move them to the new Mac from the Windows computer but that is a separate issue from removing them from the phone. Also, you can't move them via going from the old computer to the phone and then on to the new computer using iTunes. You could do that using a 3rd party app but you would lose quality of the photos on the new computer. You should move the photos from the old to new computer the same way you move other data.
Note that if you want to keep them on the phone you could first move the photos from the old computer to the Mac and then sync to the Mac with the photos selected. It should delete the old ones and replace them with the new sync.
If you just want to delete them from the phone, have you tried to do that by going to the Photos page on iTunes with the phone connected and removing the checkmark in front of "Sync Photos From" and then syncing? Note that each time you sync via iTunes it should set the non-Camera Roll photos on the phone to match the current iTunes settings.