Why does a nesting sea turtle release fluid from around its eyes while it is on the beach?

Answer: To release excess salt that it has taken in with seawater

To cool its head and eyes in the hot beach sun — The hot beach makes cooling feel plausible. But the fluid is saltier than seawater, which points to ion export rather than temperature control. The eye gland's job is chemical balance, not cooling.

To release excess salt that it has taken in with seawater ✓ — Sea turtles take in seawater while feeding, and glands near the eyes release the excess salt in a concentrated fluid. That is why the turtle looks like it is crying. The useful job is keeping internal salt lower than the surrounding ocean.

To rinse away sand and grit that collects around its eyes — Sand near the eyes makes rinsing plausible. But the salt load comes from feeding and living in seawater, and the eye is an exit route for that salt. Cleaning away grit does not explain why the fluid is saltier than seawater.