I would call that "gunk" sitting to the back (under the chip) and in between those pins, rather than "corrosion." That gunk could consist of a variety of things, including leaked capacitor fluid which you were able to clean off outside the chip but not underneath. I've seen this gunk before in my own experience. What I do is take a very tiny ice-pick shaped metal tool (about the thickness and shape of a wooden toothpick) and ever-so-slightly scrape in between each pin of such IC's, far back enough under the chip to ensure that no two pins are directly connected together by the gunk. (For chips that have a very tight pin spacing, I sometimes use an XACTO knife -- but such requires even more skill that metal pick, since you don't want to cut into your board -- just scrape away the gunk!) The gunk is not likely causing an electrical short between the pins that would fry the chip, but stray capacitance is a concern especially since some of that gunk is spilled capacitor fluid. So I would advise you to carefully scrape it away between each pin.

Before you scrape though, be sure you've don't your best to clean it off with alcohol outside the chip. I use a toothbrush and electronics grade dehydrated Ethanol for that task. That combination works so well to solidify the gunk that I don't have to do much scraping at all to clean the gunk away between the chip pins.

Lastly, I've read stories from many people here who merely clean the board and expect it to work like new. Yes, that does give the appearance of "restored operation" for a time on some boards, but the fact is, leaked fluid means your caps are either dead or at a diminished capacity. In any case, they all need to be replaced. Do not expect your machine to work properly until you do that. And yes, I am fully aware it is not a fun or quick job. But it is a necessary one.