Demurred (intransitive verb): 1 archaic: delay, hesitate
2: to file a demurrer
3: to take exception: object—often used with to or at (Merriam-Webster)
Found on Page 53, paragraph 2 of “The Cottagette”–>One day he came around early and asked me to go up Hugh’s Peak with him. It was a lovely climb and took all day. I demurred a little, it was Monday, Mrs. Fowler thought it was cheaper to have a woman come and wash, and we did, but it certainly made more work.
I believe this word in the quote means that Malda hesitated to go out with Mr. Matthews because she was mostly concerned about the home being washed by another woman. Previously, it states that Malda preferred to wash the dishes by herself, so bringing someone else to the house made her apprehensive because she did not know how this woman was going to clean her home.