“Getting into a scrape” means to be in a difficult situation and is as old as England itself.
When that country was a primeval forest, it was overrun with wild deer.
To avoid hunters, these deer would use their sharp hooves to scrape deep gullies into the ground, where they would huddle for cover.
In time these would become overgrown and difficult to detect, so while out in the forest it wasn’t uncommon to fall into a scrape.