How would you symbolize "change"?

How about a delta character? Δ
Or, how about the +/- character? ±

Maybe ± or ~ might work? ± because the change can be indicated as "Delete old, add new".

Or ask the Unicode Consortium to add the Barack Obama symbol to the standard. (Sorry, couldn't resist the title)

How about ✍ (U + 270D) or ✎ (U + 270E).

If you are limited to ASCII I would use ">" as it stands for forward movement. There are tons of characters in Unicode for you to choose from (I've always wanted to use a word, lots of: -).

^

perhaps to symbolize "UPdate"?

Do you have enough space for small icons? I would squeeze them if possible.

I would avoid anything that has an existing mathematical or logical meaning (+, -,!, Etc.). You don't mean that the hat change has changed, but for me the old "means a change, like x, x" etc. (Although this can be interpreted as output).

What about:

¢

the * sign is used in some software (VS, SSMS ...) to mark a document that has been modified but not saved ... I also like Δ, but that depends on what is curious (= how mathematical thinking ) ppl uses software

so speaking in terms of "expected behavior", I would go for * as well, as VonC already wrote.

(The first thing I thought about reading the ur header was a little Obama gg icon)

IMHO, three dots are a good indicator for edit / change commands.
Like this:

...

EDIT : I just realized that you asked for one character. But that won't delete as you might like it.