You indicate that this is for a US audience, and this would be the appropriate wording in American procedural terminology. "Trámite de contestación a la demanda" refers to the filing of the respondent's answer to the petitioner's complaint. The basic vocabulary of Spanish civil procedure is expressed in American English as follows:

--demandante--plaintiff
--demandado--defendant
(For divorce proceedings, this would be "petitioner" and "respondent")
--demanda--complaint
--contestación a la demanda--answer (to the complaint)
--reconvención--counterclaim
--contestación a la reconvención--reply to counterclaim
--declarar en rebeldía--declare in default
--sentencia dictada en rebeldía--default judgment
etc.

Your text says: "Having filed an answer to the complaint pursuant to the provisions of..."

Here are some examples:

Having filed an Answer to the Complaint, Vetter submitted himself to that same jurisdiction. B. In A Medical Malpractice Case If A Defendant Files An Answer ...
www.vamedmal.com/library/grace-lents-dpm.cfm

the Court finds that the myriad of explanations offered by Defendant for not having filed an Answer to the Complaint or a motion to vacate default...
law.justia.com › ... › August, 2007

appellants, without having filed an answer to the complaint, made a motion under Code Ann. 81A-112 (f) to strike three paragraphs of ...
vlex.com/vid/mock-et-v-copeland-20465162

The only explanation offered by defense counsel for not having filed an answer to the complaint before entry of a default judgment was that, ...
pa.findacase.com/research/wfrmDocViewer.aspx/xq/fac...0043127.../qx