My wife has professional experience at this kind of thing. For what you're doing, you won't be able to charge much, maybe $50.00-$100.00. (like someone said, 1hr work @ whatever rate) It's a little questionable to be altering the work done by the woman... I hope the company has full rights to the design. They probably do, but I'm just sayin'...
As long as they pay you, preferably up front, don't worry about getting it in writing.
My wife's boss (at a bridal salon) wanted her to make a store logo for letterhead & stuff, but she refused b/c he wouldn't pay her what that's worth. Making the logo for a business, which the business will then use in all its media, is a big deal. If you're certain they are only using it as an internet banner, and not as their company logo, then go for it.
You might ask them, but I doubt you have to slavishly copy the font--after all, it doesn't match the font in the image! (i.e. "Wide Awake" doesn't match the "union, liberty, honor" font) Not to mention it should be "unity" instead of union, whatever. Good Luck.
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