I just noticed that User Defined Table Types do not show up in sys.objects by the name you have given them, you have to look at sys.all_objects and Name LIKE 'TT<Your Type>%' or the Type_Table_Object_ID = Object_ID to find the actual object.
And surprise, surprise - the object is under the 'sys' schema.
-- Find ID in sys.table_types
WHERE Name = '<Your Type>';
-- Entry in sys.objects
WHERE Name LIKE 'TT%<Your Type%' -- or OBJECT_ID = column value under Type_Table_Object_ID from above;
And, oddly, note that the definition in sys.objects has the is_ms_shipped flag set to 1 ! Not intuitive.
Seems like a flaw.