The source is p.95 in...
Plain-Song (Helmore, Thomas) https://imslp.org/wiki/Plain-Song_(Helmore%2C_Thomas)
...and the particular sharp is this one highlighted in yellow...
It confusing, because all the other accidentals under the score match up with an accidental in the chord above, and IF the sharp means play a
D major chord, that would raise the second degree in Phrygian, which seems to un-do the Phrygian-ness of the music. (It sounds nice to me either way
D major or minor.)
I didn't mention musica ficta specifically, but I think this should be added.
In the Renaissance accidentals were not written in the notation, but in performance they were used and the practice was called musica ficta. Modern notation shows where those accidentals go above notes not on the staff.
This accidental below the note looks similar to the modern notation for musica ficta. The confusing things is how some of those accidentals are given both on the staff and below. This particular sharp is not on the staff, only below.
If I treat it like a kind of modern notation of musica ficta, I would apply the sharp.
It probably is more obvious to say the accidentals below the staff are in the same place as the figured bass symbols. A sharp alone in figured bass means to play a major third.