The year "1850" combined with Shard's reading from the notebook implies that Detective Sparrow and his contact meeting in Karas Mountain likely occurred annually. This suggests that since the "grey-headed eagle" appeared in Moon Bay over a decade ago until 1850, the meetings persisted.
From this deduction, there's a strong possibility that even before Detective Sparrow's incident in 1853, their scheduled meetings didn't cease.
Thus, it's highly likely that the contact already knows of the change with the "grey-headed eagle." Since Sparrow Hamilton's death happened a year ago, and Shard hasn't been to Karas Mountain for a meetup during this year. Of course, it's also possible the meetings occurred biennially.
"So, even if I were to stake out Karas Mountain now, I likely won't wait for the contact to show up..."
Thinking this, Shard put down the photo and said to Luviya on the other side of the desk, who was reviewing "A Thousand Kinds of Fungi and Detoxification Guide":
