
Certified GKH Gardening Expert
It could be dirt. It is very hard to say without a closeup. We cannot zoom in on the pictures, so I cannot see close up. This can happen when rain splashes dirt on the leaves, but I do see signs of distress.

Certified GKH Gardening Expert
It resembles spider mite damage. This will need to be taken care of before the problem gets too out of hand. Here are some articles that will help:
https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-control.htm
The aftermath will be fungal or bacterial infections. You will want to go ahead and treat for that.
Here are some articles that will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/garden-how-to/info/homemade-fungicide.htm
Here is an article to help you to grow Fig trees in container:
https://www.gardeningknowhow.com/edible/fruits/figs/growing-figs-in-pots.htm

I have checked for spider mite as described but it does not seem to be that. It looks like dirt residue on the leaf that I can rub or scrape off.