When using Puppet Warp (Edit > Puppet Warp) remember to look at the Options Panel, where 3 menus will give you options on how to apply the mesh.
Mode: Lets you decide how stretchable you want the mesh to be.
Density: Controls the spacing of the mesh’s points. Adding more points makes your edits a lot more accurate, but the processing time takes longer to complete.
Expansion: Expands or contracts the outer edge of the mesh.