I believe it means to make a small puncture in the parchment with a pricker, rather than mark it using ink (a quill, inkwell and blotter might have been awkward and/or messy to use). See definition 2 of "prick" in the The Concise Oxford Dictionary of Current English (1919): "mark off (name &c. list) with a prick, select (sheriff) thus."
See also page 39 of Shakespeare Quarterly (1956), "...'prick off': 'to tick off on a list' (NED 15)," in which "NED" stood for New English Dictionary (the original title of the Oxford English Dictionary).
Apparently, it was also commonly used in surveying to create copies of the plans by laying the original map or plan over a blank paper then making small holes at key locations which could then be drawn by connecting the dots (A Complete Treatise on Practical Land Surveying).
The usage is archaic since we have more portable writing instruments now but not that uncommon for the time period the book is set in. It's used in a variety of topics:
The Statutes at Large of South Carolina: Acts, 1716-1752
Design and Construction in Wood
The Young Surveyor's Guide
What I found much harder to find was the strange use of sheriff in the definition above. It seems to have been an obsolete form of shrieve, which is an obsolete form of shrive. According to the Online Etymology, shrive comes from the Old English scrifan, which among other uses was "apparently originally 'to write'."