In your above example as per doc , Map's remove method takes in only one key as argument and returns a value as return type. you cannot pass a list of strings to the remove method, though I tried something like below based on java's removeall ( undocumented in salesforce map methods )
https://stackoverflow.com/questions/17675804/remove-multiple-keys-from-map-in-efficient-way
http://www.salesforce.com/us/developer/docs/dbcom_apex250/Content/apex_methods_system_map.htm
Map<String, String> colorCodes =
new Map<String, String>();
colorCodes.put('Red', 'FF0000');
colorCodes.put('Blue', '0000A0');
colorCodes.put('Blue2', '0000A0');
set<string> remove_keys = new set<string>{'Red','Blue'};
colorCodes.keySet().removeAll(remove_keys);
system.debug('#### Map after removing keys'+ colorCodes);
13:30:38.052 (52492111)|SYSTEM_METHOD_ENTRY|[9]|System.debug(ANY)
13:30:38.052 (52504469)|USER_DEBUG|[9]|DEBUG|#### Map after removing
keys{Blue2=0000A0}