Yes, GBL is miscible with water. However, it is also miscible with DCM. DCM is not miscible with water. So you get 2 layers, a water/gbl/crap layer and a DCM/GBL layer. If you extract with DCM several times you can extract almost all of the GBL out of the water, so you are left with only DCM/GBL. Then you distill.