Step 1: Think about what changes across the cycle.
Cervical mucus is watery and stretchy near ovulation and thick and sticky after it, so two different hormones must be pulling it in opposite directions.
Step 2: Assign the fertile phase hormone.
Just before ovulation, the growing follicle pours out estradiol. This hormone makes the cervical glands secrete more mucus and makes that mucus thin, clear and stretchy, ideal for sperm to travel through.
Step 3: Assign the post ovulation hormone.
After ovulation the corpus luteum secretes progesterone, which thickens the mucus into a scanty plug that blocks the cervical canal.
Step 4: Place the other two hormones.
Estriol is a weak estrogen important mostly in pregnancy, not in the cyclical mucus pattern. Pregnenolone is just a precursor molecule used to build other steroid hormones, it has no direct glandular action.
Step 5: Conclude.
The hormone that stimulates cervical mucus production is estradiol.
\[ \boxed{\text{Estradiol}} \]