“Forego” with an “e” means to precede. Think of the “fore” as “before.”
So, essentially, this headline tells us that the Humane Society shelter went before a $50 fee. That, of course, makes no sense.
What the headline writer meant was that the shelter decided to “forgo,” or do without, the fee.
American Heritage lists “forego” as a variant spelling of “forgo.” (The Associated Press stylebook, on the other hand, makes a clear distinction between the two.)
There’s a reason I emphasize variant. You can always argue that a variant spelling is correct. Why rely on technicalities, though, when you can be precise? Using “forgo” makes the meaning clear. That’s what all writers and editors should aim for.