"Te Lo Agradezco, Pero No" is the second duet recorded by the two singers, following "La Tortura" for Shakira's album Fijación Oral Vol.

"Te Lo Agradezco, Pero No" was written by Alejandro Sanz for his album El Tren de los Momentos (2006).

[2] "Te Lo Agradezco, Pero No" marks the second time Sanz and Shakira collaborated after "La Tortura", included on the latter's Fijación Oral, Vol.

[4] Two of them — one done by Luny Tunes and the other one dubbed "Benztown Mixdown" — were included on the re-release of Sanz's album in 2007, El Tren de los Momentos: Edición Especial.

[5] In a review of El Tren de los Momentos, Jason Birchmeier of AllMusic pointed out "Te Lo Agradezco, Pero No" as a highlight on the album.

[7] Chuck Arnold, Ralph Novak and Monique Jessen, writing for People magazine, also pointed out the track as one of the best on the record, adding that the duo managed to "again bring the tropical heat" with it.

[3] David Saavedra, a critic of the Spanish newspaper El Mundo, found elements of Latin flamenco in "Te Lo Agradezco, Pero No" and noted how it was a proof of Sanz's departure from his early-career material.

[12] The recording further was nominated in the category for Best Vocal Duet or Collaboration at the 2008 Latin Billboard Music Awards, but lost to "Pegao" (2006) by Wisin & Yandel.

However, in "Te Lo Agradezco, Pero No", the roles of Sanz and his love interest change and he clarifies that "there are no promises that are worthy after everything is finished".

A making-of clip about the music video was included on the DVD of El Tren de los Momentos: Edición Especial (2007).

[26] "Te Lo Agradezco, Pero No" was part of the set list of Sanz's seventh El Tren De Los Momentos Tour (2007–08) which visited countries in North and South America and Europe.