**Core Concept**
The progestogenic emergency contraceptive pills work by inhibiting or delaying ovulation, thereby preventing fertilization. This is achieved through the action of progestins on the hypothalamic-pituitary-gonadal axis, specifically by affecting the release of gonadotropin-releasing hormone (GnRH) from the hypothalamus.

**Why the Correct Answer is Right**
Progestogenic emergency contraceptive pills, such as levonorgestrel, work by inhibiting the surge of luteinizing hormone (LH) release from the anterior pituitary gland. This LH surge is essential for ovulation, and by preventing it, the progestins delay or prevent ovulation, thereby preventing fertilization. The mechanism of action of progestins in emergency contraception is primarily through the inhibition of LH release, which is mediated by the action of progestins on GnRH release from the hypothalamus.

**Why Each Wrong Option is Incorrect**
* **Option A:** While progestins do affect the hypothalamic-pituitary-gonadal axis, their primary mechanism of action in emergency contraception is not through the inhibition of follicle-stimulating hormone (FSH) release.
* **Option B:** Progestins do not primarily act by causing an increase in progesterone levels in emergency contraception.
* **Option C:** Progestins do not primarily act by causing an increase in estrogen levels in emergency contraception.

**Clinical Pearl / High-Yield Fact**
It is essential to note that progestogenic emergency contraceptive pills are most effective when taken within 72 hours of unprotected sex, and their effectiveness decreases with increasing time.

**Correct Answer: C (Progestins delay or prevent ovulation by inhibiting the surge of luteinizing hormone release from the anterior pituitary gland)**