They are asking you to execute a function on their smart contract that will initiate the refund. In order for you to be able to do execute that function you do need to enter the contract ABI and you will need to sign the transaction with your account.
So, what they are asking for your to execute a transaction on their contract is normal. Now...
Make sure that you are being directed to the REAM MEW. If they sent you the link over email, don't use that. Go ahead and enter MEW's url directly. Clicking on email links is how you fall in phishing scams. Also, make sure this ICO has issued this statement from their official channels and it's not just an isolated communication.
Anyways, the process they are asking you to do is perfectly fine. BUT, if the MEW link is a phishing site, using your json keystore file will compromise your account.
Also, if the ICO team is up to no good, calling this function might do something you don't want. The risk here is very low as you would not be sending ether again. You already gave them your ether before, if they were up to no good (flight risk) calling this function will not do further harm. I'd still try to give the smart contract a reading to make sure the function you are being asked to execute does what they say it does.