Garbado is a less common, more poetic way to say "engraved" or "etched into memory." While grabado is the standard past participle of grabar (to record/engrave), garbado appears to be a unique, perhaps regional or artistic variation used here.
In the song, the lyric "Tengo garbado en mi memoria tu triste partida" (I have your sad departure engraved in my memory) uses this word to powerfully convey the lasting impact and deep impression of a loved one's departure. It suggests a memory so profound it feels physically etched into the singer's mind, making it a memorable and evocative choice.
Fonseca opens by bargaining. He asks for a thousand small thoughts a day — "Te pediría que me pienses mil veces al día" (I'd ask you to think of me a thousand times a day) — and then offers the only thing a songwriter really has: "Me inventaria cada mañana una nueva melodia" (I'd invent you a new melody every morning). By the chorus the bargaining has collapsed into an apology. "Te pido perdón / De rodillas te digo / Regresa conmigo" (I'm asking your forgiveness / on my knees I tell you / come back to me).
What he keeps circling back to is what her leaving left in the room. "Dejaste mi cuerpo temblando y vacío" (You left my body shaking and empty), and a house that reads as empty even with people in it — "Voy a esta casa aunque este llena se siente vacia". The third verse repeats the chorus word for word, adds nothing, and leaves him still on his knees as the song fades.