The damage - if you consider it damage - has been done. Some people willingly freeze ginger to store it for long periods (up to a year) while others find it soggy once thawed. Since it's already frozen, leave it as is and just break or cut off pieces when you want to use it and return the rest to the freezer (well wrapped in a heavy plastic bag). You can grate it quite easily while it's still frozen.

To save ginger for more than a few weeks anyway, you would either have to freeze it or peel it and store it in a jar of vodka or sherry, which, to us, seems more drastic than freezing it in the first place. Where ginger is a luxury, we're sure a change in texture that might drive the food snobs wild will seem like a small price to pay.