Everything applied to a strop affects its draw. Being conservative is a good idea because one would not want to try something that does not work out and cannot be reversed. One can always try a more aggressive technique later, if conservative does not work.
What has worked for me is surface cleaning with a damp cloth and hand rubbing. All my strops were flexable to start. None were stiff, hard and dry, or old in need of restoration. When using a treatment, I would use less, go slow, and only add more later if clearly needed.
I rub my strop post shower before shaving the again after shaving and stropping. This is to remove any grit as well as oil the leather. Too much oil from the skin can build up a film of crud that can affect draw and trap grit. The damp cloth will remove the film of crud.