Burn option and requirements

The Rulebook says:
Some cards that have a requirement also have a burn option icon. This icon means that a Methuselah who doesn't control a minion that meets the requirements may discard the card during any Methuselah's unlock phase. Each Methuselah is limited to one such discard each unlock phase.

If I control Teresita (Black Hand Seraph) with Tattoo Signal on her, may I use burn option on the second Tattoo Signal in my hand, since the vampire can have only one Tattoo Signal and I have no other Seraph in play?

If "yes" or "no" - why?

No, you can't because you meet the requirements. The requirement is "a seraph", not "a seraph with no tattoo signal" (cf. With Legacy)