My cousin was feeding the leopard gecko a cricket which was dusted with calcium. Some of the calcium got in her left eye. Could this cause any health problems?
Assuming the main component of the calcium powder is Calcium Carbonate, a common chalk-like salt, you can take a look at this question on ChemistrySE.
They link to its MSDS, the safety sheet outlining potential dangers of chemicals. In eye contact they mention:
Check for and remove any contact lenses. In case of contact, immediately flush eyes with plenty of water for at least 15 minutes. Cold water may be used. WARM water MUST be used. Get medical attention.
Best would be to 1) spray loads of water on the gecko to rinse their eyes, either by using a fine mist, or by dripping water into the eye directly (depends a bit on your willingness to restrain the animal) and/or 2) bring them to a vet.
For future feedings, you might want to consider gut-loading (or a wiki how) your crickets first. Gut loading is the practice of having a food item, like mice or crickets in this case, eat the supplements for the pet. This way the supplements reach the pet in a nice "packaging" instead of on the outside of the food item, where this kind of accidents can happen.
Crickets will eat practically anything, included powdered milk. If you want to introduce calcium to your gecko's diet, then you could feed the crickets some powdered milk 12 hours before feeding them to your gecko. This will prevent the need to dust crickets, which will prevents accidents such as this.