The sentence is not fully idiomatic in my opinion but the meaning of desconocer is pretty clear: to do not know.
According to the DLE:
2. tr. No conocer.
I've not read the article but the sentence provided means that the couple decided to send the bottle because they have found something amazing, something that they thought was unheard-of.
According to the Cambridge Dictionary:
surprising or shocking because not known about or previously experienced
Probably it's a case of poor translation because the object used with verb desconocer does not need the preposition de (which is present in the word unheard-of).
Being unheard-of their discovery, they decide to send a message in a bottle. Or, using the same order,
They decided to send a message in a bottle because their discovery was unheard-of.
A more idiomatic version of the sentence would be:
En aquel entonces, la pareja decidió enviar un mensaje dentro de una
botella al río desde una orilla cerca de su casa al desconocer un
I've replaced the preposition tras. It doesn't mean because in Spanish which it's the word that the text seems to imply. Particle al plus infinitive does imply a causal sense in Spanish.