Praise be to Allah.
Singling out Rajab for fasting is makrooh, so this woman made a vow to do something makrooh. If a person vows to do something makrooh, then it is better for him not to do it and to offer kafaarat yameen (expiation for breaking a vow). So she should offer kafaarat yameen by freeing a slave, or feeding ten poor persons, or clothing ten poor persons, giving each poor person half a saa’ of food, or clothes that are acceptable for praying in. If she cannot do any of these three things, then she should fast for three days. This is better for her, and she should not do what she vowed.