As an alternative, you can head to your local hardware store, pick up a 1/4-28 tap, suitable tap drill, and a couple of 1/4-28 socket head sap screws long enough to go through a socket fitted over the base of the brass to rest on the bottom of the die and take it out yourself. Piece of cake.
That said, after you get it out I'd recommend taking a piece of dowel rod that's about 1/2 to 2/3 the diameter of the sdie body at the shoulder, sawing a slit in the end of it, to hold a strip of emery paper about an inch wide, chucking it in an electric drill and using some emery paper soaked in oil to polish the inside of the die. I've had stuck cases in Redding does on several occasions/. After polishing the inside of the die with 400, 600, and 800 grit paper for 20 to 30 seconds per grit your problem will be history. You can get the paper at an automotive parts store in a variety pack that has several grits) they never stuck again. The worst one I had was my .223 Rem. FL sizing die. That was sticking about every 20th case. I polished it and a few thousand cases later it hasn't stuck again.