Hydrodynamic extrusions of tethers from giant unilamellar vesicles (GUV) enclosing a poly-N-isopropylacrylamide (polyNIPAM) gel are studied. The collapse of the gel upon heating induces a deswelling of the GUV, showing that the membrane is linked to the polymer network. The gelly vesicle is attached to a micro-rod and submitted to a flow (velocity U). Above a threshold velocity (U >Uc) a tether is extruded and reaches a stationary length L ≃0U in a characteristic time 0. The vesicle behaves like an entropic spring with a tether length L proportional to the Stokes friction force. Compared to viscous “sol” vesicles, gelly vesicle are much stiffer: L and 0 being hundred times smaller. We conclude that the mobility of lipids is reduced, only a small portion of the vesicle area being free to flow into the tube.