He wasn't blessed with the gift of mind reading, so he didn't know what she was thinking. Yet, some things were easy to guess. If Flossie Wright didn't even know why she was being followed, then all the capabilities she had shown in the past couldn't possibly be authentic.
"Here you go," she pulled out the piece of paper from her pocket without any hesitation and handed it to Glenn Hutchinson, "this is it".
She didn't need to be secretive around Glenn Hutchinson. It's not that she trusted him unreservedly, though she did to a certain extent, but that wasn't the main reason.
After all, Glenn Hutchinson was a special forces captain. Although Flossie Wright wasn't very fond of the forces from her heart, it didn't shape her perception of Hutchinson's skills and what he was capable of doing.