The conjugation of reflexive verbs is as follows: Comerse Yo me como Tú te comes Él se come Nosotros nos comemos Ustedes se comen Ellos se comen. Now, you have to take into account that in those conjugations there is reference to the object that has been eaten. If you add it, you can add the noun itself, or a pronoun (la, le, lo) Yo me comí la tarjeta = yo me la comí. Tú te comiste la tarjeta = tú te la comiste. Él se comió la tarjeta = él se la comió Nosotros nos comemos la tarjeta = nosotros nos la comemos. Ustedes se comen la tarjeta = ustedes se la comen. Ellos se comen la tarjeta = ellos se la comen. In all those sentences, every single one uses the proper reflexive form (me, te, se...) and "la tarjeta" as object noun, or "la" as object pronoun. The sentence is "el cajero automático se ha comido mi tarjeta", "el cajero automático" is the noun conjugating the verb "se" is the reflexive form, "ha" is the present perfect using the verb "haber" (third person singular "el ha"), "comido" reflexive verb in past participle, "mi tarjeta" objective noun. In the sentence "el cajero automático se la ha comido" is exactly the same, the only difference is that is uses "la" which replaces "la tarjeta", thus, it is an object pronoun. "El cajero automático se la ha comido mi tarjeta" makes no sense because you are using the object pronoun and the noun referring to the same noun, it would be like saying in English "the ATM has swallowed it my card", you can you "it" or "my card" but not both... same in Spanish. I hope this helps.

I think the explanation will be better with some examples: El cajero se ha comido mi MI TARJETA". El cajero se LA ha comido. "The ATM ate MY CREDIT CARD" The ATM ate IT. "La" is replacing "mi tarjeta". We use the personal pronoun's reflexive form "Se" (3rd person) this way: The toy broke. El juguete SE ronpió. This clock has stopped. Este reloj SE ha parado. We often use reflexive pronouns: I get tired easily. (Yo) ME canso con facilidad. Do you like chocolate? ¿TE gusta el chocolate? I think It must be really confusing. I wish I could explain it to you in a better way.

Both sentences are not fully correct: El cajero automático se ha comido (a) mi tarjeta El cajero automático se la ha comido (a mi tarjeta) Firstly, "comido" is not followed by the preposition "a", if it is not a person or animal: El cocodrilo se comió al explorador. (a+el) (if we mencioned that explorer before) El cocodrilo se comió a un antílope. And secondly, "la" and "mi tarjeta" works as the same concept "it", so you have to use just one of them. The word "se" is a pronoun used in Pronominal Verbs. Some Spanish verbs could work in this way. Check them for more information.