If you have mistakenly made an ETH withdrawal from your Gatecoin account to an external ETC wallet address, you can recover them using one the following options:
1. Since the ETC chain is a fork of the ETH chain, any private key on the ETH chain is equally valid on the ETC chain and vice versa. Therefore, you can run an Ethereum client on the ETH chain and import the address that holds the funds and the ETH balance will show up under your wallet.
2. If you're currently not running your own ETH/ETC node and this is an address you never plan to use again you might consider using MyEtherWallet.com and import the private key of your address. You will be able to import your keystore file into MyEtherWallet and the ETH which have been wrongly sent to your ETC address should appear. You can switch between the ETH/ETC chain in the website and you will be able to see your balance in each chain.
If you decide to go for the second option, please make sure to follow MyEtherWallet's general safety tips to double check the URL and the SSL certificate to make sure that you are on the official website.