Step 1: Recall the male duct system.
Sperm made in the seminiferous tubules pass through the rete testis, then the vasa efferentia, then the epididymis, and on to the vas deferens.
Step 2: Check rete testis.
The rete testis is a network of tubules that collects sperm from the seminiferous tubules. It is part of the male system, so not the answer.
Step 3: Check vasa efferentia.
The vasa efferentia carry sperm from the rete testis into the epididymis. They are male structures, so not the answer.
Step 4: Check epididymis.
The epididymis lies along the back of the testis and stores and matures sperm. It is clearly male, so not the answer.
Step 5: Check infundibulum.
The infundibulum is the funnel-shaped opening of the fallopian tube near the ovary, which is part of the FEMALE reproductive system.
Step 6: Conclude.
Since the infundibulum belongs to the female tract, it is the structure that is not part of the male reproductive system.
\[ \boxed{\text{Infundibulum}} \]