Took me a few reads, but it's actually quite simple.

You want a structure that can tell you something has been seen, but sometimes forgets, but will never incorrectly tell you something has been seen.

Solution: an array. Hash the item to find its index, swap out what's there, and see if it is your item. If so, you know for sure it was previously placed. If not, then it might not have (it may have been forgotten).

  let arr = Array of key
  let contains_key key = 
    let index = hash key % arr.length
    let prev_key = arr.swap[index, key]
    return prev_key = key

The hash algorithm is crucial. Reducing forgetfulness is as simple as making the array longer. And he points out that if you can compress the keys, you can reduce storage size.