Declaring the type of 'this' in a typescript function?

Now (from TS 2.0) you can specify function's this type by using fake this parameter (should be the first one):

grunt.registerMultiTask('clean', function(this: SomeType) {
    //...
});

this parameters are fake parameters that come first in the parameter list of a function

More info here

How do I tell TypeScript to consider this to be a different type

You can do that by declaring a this parameter. For your use case I've added this: {files:any[]}:

grunt.registerMultiTask('clean', function(this: {files:any[]}) {
    this.files.forEach(function(f) { Delete(f); });
});

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