OK,? Pictured below is the Star Die Removal kit (this one purchased from Magma Engineering)
1.) Remove the bullet punch, and install Part A where the bullet punch used to be.
2.) Thread Part B into Part A.
3.) Lower the handle to push out the bullet that remains in the sizing die.
4.) Remove Part B from Part A, and thread Part C up through the sizing die and into Part A.
5.) Lift the handle, pulling out the sizing die.
You may need to heat up the Lubrisizer as you would for sizing in order to accomplish the above steps.
Actually, I never use the kit, I just use a wooden dowel to push the sizing die up with my knee.