Firstly, Yumeko will not read this letter, but will pass it on to Mistress Shinki. But.. Your story does not add up. If Lady Alice would hire a mercenary to deliver a simple letter, Yumeko does not believe that the mercenary was not prior informed to not trespass. Yumeko is also highly suspicious of a strange male carrying a letter, claiming to be from Lady Alice. Lady Alice only has two known acquaintances outside of this family. And neither of them are male. Regardless, your note will still be passed on.
Secondly, Yumeko is highly insulted that you decided to comment on her working capabilities. Yumeko was on duty outside of the Fortress, and was informed of an unknown presence by the worker who /should/ have halted you. Yumeko would have preferred to have gotten here before you walked three meters through this doorway, but Yumeko can only run so fast.
Thirdly, Yumeko will show you the way out. Yumeko will not leave any suspicious persons unattended in Mistress Shinkis abode. Make any movement that is unnecessary, and Yumeko will remove one part of your body for each suspicious act.