Archery had largely passed out of military relevance In England by the time the English started to colonize North America. But there was still plenty of archery equipment around (some bows were even brought to the New World, although I don't think they were ever issued). But the time when archery had been of military importance and was an active part of English social life in towns and villages was still easily within living memory. People in Tudor England were absolutely shooting bows for recreation even though the bow was increasingly viewed as a military anachronism. English colonists would undoubtedly have known what bows were and recognized their potential threat.

Of course; we haven't used bows in warfare for hundreds of years yet we still know what they are. We also don't use cavalry, or plate armour, yet you would recognize a knight wouldn't you? Julius Caesar invaded Britannia hundreds of years since chariots went out of fashion in war, yet he and his soldiers still recognized the archaic devices used by the Britons. This is but one example.

Point is, just because something hasn't been used for some time doesn't mean that people immediately lose all knowledge of it. This isn't a question of historical knowledge as much as general knowledge. If you need reasoning behind it; in the time of the Tudors bows were also used for recreational purposes, and undoubtedly used for other purposes, such as hunting. They are, after all, a very early human invention and used by almost every civilization and ethnicity on the planet!