You may be mixing two separate customs together.


Quoted in Taamei Minhagim (pg. 521 paragraph 68), saying he saw it in some Sefer:


There is a custom for women to bite off the pitum of the Etrog. The reason is because our sages say that (according to one opinion) the forbidden fruit Adam and Chava ate was an Etrog. Therefore she bites the Pitum in order to show that "just as I have no benefit/pleasure from biting a Pitum so too I had no benefit/pleasure from the sin"


[Notice he does not say anything about Hoshanah Rabba]
Two parter brought in the Kaf HaChaim 664:60, and was mentioned in my answer here:


There is a custom to take the Etrog used on Sukkot, turn it into Etrog Jelly, and eat it on Tu B'Shevat.
There is a custom for pregnant women to eat Etrog Jelly while in labor, as a Segulah for an easy labor, and children that grow up with a good and peaceful life.





Or perhaps not, since the custom is mentioned explicitly in Likutei Maharich Part 3 (pg 106A) by Yisroel Chaim Friedman. (as linked to on the webpage quoted by yydl in the comments to the question.)

What does biting off the Pitum have to do with Pregnancy?
I am taking an introductory course on python and the instructor says that python is a high level language and C and C++ are low level languages. It's just damn confusing. I thought that C, C++, Python, Java, etc were all high level languages. I was reading questions at stackoverflow on C, C++, etc and they all seem to refer to those languages as high level. it seems to me that some programmers use those terms interchangably. Please clarify this for me.
