Based on the photo, these eggplants have substantial areas of damage and so I think the calyx browning is the least of your worries.  In my experience the calyx browning is related to water lo

A good reading of our Eggplant Produce Fact Sheet should be helpful to you. At a temperature of 14-16°C, dehydration will likely lead to browning of the calyxes and the impact of ethylene will