I'm not sure what you mean by A spider + 's landing pad. Are you asking if "A spider's" could be short for "A spider is" or "A spider has"? If so, do you think that works given the other two words in the sentence?
By the way, in what way did he use it as a joke? I can't see anything remotely funny about it and I cannot imagine what he was referring to.
Student or Learner