The given clause, "whoever wins the contest a savings bond" is a subordinate or a dependent clause. This kind of clause does not convey a complete thought and needs the main sentence in order to make it understandable. This subordinate clause is connected to the main clause with the subordinating conjunction "whoever".
Holden doesn't feel bad about leaving the school because school wasn't important to him. ... Holden visited Mr. Spencer because he was a teacher that he liked. He regrets visiting Mr. Spencer because he hated being pointed at for example when Mr. Spencer read his paper in front of Holden
