There are a lot of differing opinions about footer links, particularly how to optimize them.
One camp says that these links should be innocuous, brand-name only links (i.e. alt tags that are your domain name or corporate name). Too many optimized inbound links (or alt tags on images that link to your site) could cause some sort of over-optimization penalty. While I think this is solid advice, I too have seen companies use highly optimized site-wide footer links, and they seem to be beneficial...so I'm not inclined to say that footer links shouldn't be optimized at all.
Another camp argues that you should go ahead and optimize all the link text, but to do so slowly and naturally. My concern with this approach is outlined above...at some point, you're going to have dozens or hundreds of links pointing to your site with optimized text/alt tags. That's not necessarily natural.
A middle-of-the road approach is to just change some of the links, and if I were you this is how I'd start. I'd identify the most trusted sites, change the alt tags on half of them to something optimized, then sit back and wait 3 months.
Additionally, I've always been of the opinion that one good footer link on a website's homepage - or an in-text link on the client's "about" page - is more valuable than a site-wide footer link. While I don't have any proof of this, it's something you might test. On sites we design, we like to put an "about this website" sub-heading on the client's about page, then link to our site in that text. It seems natural to me, and my site does OK.
Anyways, good luck. Whatever you do, I think gradual change is the key.