I am very fussy about this sort of thing but I don't think those brown marks are a problem. They are usually on the edges and will not come into contact with the food you eat. Definitely don't use anything abrasive.
Having said that, I stained TWO Pyrex dishes badly last night. DH was out and I thought I'd just make a handful of popcorn and took a Pyrex dish with a lid and popped it in the microwave but I set it for too long a cooking time and ended up with a black charcoal mess and only by opening all the windows and shutting the doors could I prevent the smoke alarm from going off. The second dish I set at half the time but it was still too long and produced the same results. I did feel silly - I've made Popcorn in the microwave often enough before! Having run out of dishes with fitting lids, I ended up doing it the conventional way, in a saucepan.
I took the dishes and lids, which were black, out into the garden (in the pouring rain) and sprayed them with oven cleaner, leaving them on the table out there all night. I must go out now and see if the rain and the oven cleaner have got any of the burn marks out.