This practice is also brought down by Simla Chadasha (11:10); see the מטה אשר there (12) who brings from the פלתי that this practice is from ר' יהודה החסיד and was only a concern then, because in his time there were many who practiced כישוף (magic) on geese, but is now no longer a concern.
אין להקפיד ע"ז, כי אז בימי ר"י החסיד היה הזמן גורם, כי רבו אז המכשפים באווזות, אבל עכשו לית חשש כלל
One needn't worry about it, because during the time of R' Yehuda HaChassid there were many who practiced כישוף on geese, but now there is no concern at all. [translation mine]
I asked my rebbi, and he told me that one time he was shechting geese in Teves, and found himself wondering if there is still a הקפדה on this stringency of R' Yehuda HaChassid. He asked his rebbi (Rav Yisrael Belsky), and he was told that there is nothing to worry about; but, suspecting that the chassidim
might still worry about it, he also asked the Satmar Rebbe1
, who told him that even among the chassidim
, no one worries about this anymore.
....I don't know about the hearts, but not all agree that the heart of a bird is קשור לשכחה, because the only thing brought in the Gemara is animal hearts. Also, if you see the Simla Chadasha in the link, he records that while some had the custom to eat from the heart, others ate from the liver and still others from the legs2
....it's possible that those who would tell you that avian hearts are problematic for memory would tell you to eat a different part of the goose.
1 R' Aharon -- not a political statement, just an anecdotal one!
2 He ends off by saying "נהרא נהרא ופשטיה," (literally "every river has its tributary") meaning that you could really eat whatever part of the goose you want.