Question: If someone forgot to say Retzei Ve'hachalitzenu in Birkat Hamazon on Shabbat, does he need to repeat it?

Answer: If he remembers before starting Boneh Yerushalayim, or even if he started and said Baruch Ata Hashem, he should say Lamedeni Chukecha and then go back to recite Retzei. If he already finished Boneh Yerushalayim, he should say the additional text Asher Natan Shabbatot LeMenucha (which appears in most siddurim).
If he forgot entirely and already began HaTov VeHaMeitiv, if he remembers before saying La’ad, he can still insert Asher Natan Shabbatot LeMenucha. However, if he only remembers after that:

If it was the first or second Shabbat meal, he must repeat Birkat Hamazon from the beginning.
If it was Seudah Shlishit, he does not go back.
Even in the second meal, if he ate a kezayit of cake or similar baked goods before the meal, he does not have to repeat Birkat Hamazon.

This ruling applies equally to both men and women.