Learn Spanish (Spain): Que yo recuerde, ellos no han transmitido la leyenda. - As far as I remember, they have not passed on the legend.

This sentence uses the fixed formula que yo followed by the subjunctive to express limited knowledge. It translates to "as far as I remember" or "that I can remember." The subjunctive is required here because you are establishing a boundary to your knowledge, rather than declaring an absolute, objective fact.

Is it necessary to include the pronoun yo in Que yo recuerde?

Yes, it is highly recommended. While Spanish usually lets you drop subject pronouns because the verb ending gives it away, in expressions of limited knowledge like que yo recuerde or que yo sepa (as far as I know), the yo is almost always kept. It emphasizes that this is strictly your own personal perspective.

Doesn't transmitir usually mean to "broadcast" something?

It can certainly mean to broadcast (like a TV or radio signal). However, when paired with words like leyenda (legend), culture, traditions, or values, transmitir means to "pass on" or "hand down" from one generation to the next.

Why use the present perfect (han transmitido) rather than the simple past (transmitieron)?

In Spanish from Spain, the present perfect is frequently used when a past action (or in this case, a lack of action) still feels strongly relevant to the present moment. Using han transmitido suggests that their failure to pass on the legend affects the current situation you are discussing, perhaps because the legend is now entirely forgotten.