Just Salad told us by email that they use either sunflower oil or olive oil for oven-baked items, seasoning and the preparation of their dressings, and that nothing is fried. Sunflower is still a seed oil so this is not a clean pass, but plain extra virgin olive oil is sold as a standalone dressing, so a seed-oil-free bowl is possible here.
Just Salad answered by email and it is a better answer than most chains give. They said that for the items that are oven-baked, seasoned, and for the preparation of their dressings, they use either sunflower oil or olive oil, and that they do not fry any of their ingredients. Sunflower is still a seed oil so this is not a clean pass, but there is no fryer anywhere in the operation and they did not name soybean, canola or cottonseed at all. They also did not say which items get sunflower and which get olive, so I could not narrow it any further than that. Worth knowing if you are avoiding seed oils: they sell plain extra virgin olive oil as a standalone dressing and also paired with balsamic or red wine vinegar, so you can build a bowl that sidesteps the question. What they did not answer is whether the crispy toppings, falafel, tortilla chips or warm grains carry those oils, and no per-item ingredient statement exists on their site or in their ordering app.