I've looked through those registers on Family Search. I think the annotation is P T P and would hazard a guess its to do with accounting rather than illegitimacy and possibly means Private To Pay/Parish to Pay so the baptism was done privately maybe as the child was not certain to live and then entered into the register later (and possibly the rites to receive her into the congregation were carried out) but still to pay for the entry.
This one is prior to the baptism you posted
https://www.familysearch.org/ark:/61903/3:1:939N-Q7SM-K6?i=286&cc=1804330&cat=1805267(you need to be signed in to view that)
has the same notation but the child was not illegimate.
There seems to be a lot of notes like this in the registers, obviously all meant something to the parish clerk at the time but I am unsure of many of them (I've seen OF on a good few and can't guess at those)
NB this is just my best guess and not writ in stone :-)
Boo