When you debug your store you can disable PushOwl in temporarily by adding param
poTaskType=disabled to your store web address. So if your store web address is https://store.myshopify.com/ then visiting https://store.myshopify.com/?poTaskType=disabled will disable PushOwl in the store temporarily till you close that browser tab.
PushOwl will be disabled temporarily only for you. It will be enabled for others. PushOwl script will still load but it won't run. PushOwl script size is around 30KB so it should cause any delay in your store load time