No suggestions, Day does!: “a type of cross which no doubt has to do with one of the Knighthood degrees”.
Cooper calls this a “Papal Cross” which is indeed a cross with three bars, but this symbol on the scroll has a very specific form.
The exposure Three Distinct Knock (1766) has a Dublin edition (year unknown). At the end there is an drawing which includes a cross somewhat like this one. Note that most of the other symbols are on the Kirkwall Scroll as well.
Templar degrees still have a three barred cross, but I have not found any of this particular design.
