You should initial for any alteration made to the check. Article 3, section 407 of the Uniform Commercial Code, which deals with altered checks, specifies a wide array of actions that constitute an altered check, so you want to make sure that you've initialed for any change you make to the check that would constitute an "altered check" without such authorization.
(a) "Alteration" means (i) an unauthorized change in an instrument that purports to modify in any respect the obligation of a party, or (ii) an unauthorized addition of words or numbers or other change to an incomplete instrument relating to the obligation of a party.
If you need to change the amount, however, you're probably better off shredding the check. Remember that it's very easy for someone to commit fraud if they get your account number. If you don't have access to a shredder, see Victor's comment for an easy way to securely shred the check.