My dignity is...how do I put it...? Well...Only your cuteness is spewing out like a geyser, Milady.
Mmh-hm-hm!Grrr!Anyway...why is that green fox...!Well...a date...?Leaving their shrines unmanned and going on a date, who do they think they are!?Well...why don't you ask them directly?Eh...what did you say? Sakuya...say that again.Your dignity has already wilted.Eh...? Th-that's out of the question... because...you know?Yes...I understand, Milady.Phail Maid
This is mashing ダメ, which can mean failure of something when placed behind a noun, thus ダメイド is "faillure maid"