Final answer:
The flared region at the distal end of the uterine tube is called the infundibulum, with finger-like projections known as fimbriae.
Step-by-step explanation:
The term that refers to the flared region at the distal end of the uterine tube is the infundibulum. The infundibulum is the wide, trumpet-like portion that terminates in slender, finger-like projections called fimbriae. The fimbriae help to guide the oocyte, released from the ovary during ovulation, into the uterine tube. This critical region of the reproductive system plays a key role in facilitating the movement of the egg from the ovary to the uterus, where it may potentially be fertilized.