"Scoured into limp submission" refers to the Fosters' house, where Winnie lives with her family. If something has been "scoured," it has been scrubbed very hard until clean. That's a pretty good description of the Fosters' "touch-me-not" house, which is always absolutely immaculate.
As well as being clean, the house is tidy, with everything in its proper place. Winnie's mother and grandmother positively hate any kind of disorder and insist that every single object in the house be organized down to the last detail.
All well and good, but the problem with the Fosters' insistence on cleanliness and order is that it robs the house of any character. The house has no life of its own, no real identity. That is what is meant by "limp submission." The house is limp in much the same way as someone goes limp when they die. And death, in this respect, constitutes the ultimate act of submission.
It's as if the unique character of the Fosters' house has been killed by all the constant cleaning, tidying, and arranging carried out by Winnie's mother and grandmother on a daily basis. The contrast with the Tucks' cluttered, untidy, almost chaotic house really couldn't be greater. Even so, as Winnie discovers, the house, unlike hers, still has very much a life of its own. It is much more comfortable for not having been "scoured into limp submission."