Pruning the lower branches will not make the tree grow taller. All it will do is clean up the lower trunk area.

But you should be aware that dogwoods do not always respond to pruning well.....often generating a plethora of new shoots at any pruning cut. If you DO remove any lower branching - always best to do while tree is dormant - be sure to take them back cleanly to the branch collar. That should limit any errant shooting at that point.

Tree already looks stressed by exposed position and dogwoods do not like sun beating on the trunks and root zone.