Hi Emily. This verb tense is "pretérito imperfecto de subjuntivo". It's similar to "present unreal conditional"(used to talk about what you would generally do in imaginary situations.) in english. Usualy, it is used in the "if" part of the sentence, for example. Si Laura sonriera(o sonriese) más, sería más feliz. If she smiled more, she'd be happier. Si tuviera (o tuviese) un coche, estaría allí temprano. If I had a car, I would be there early. ¿Qué harías si ganaras (o ganases) la lotería? - Me comparía una casa en Madrid. What would you do if you won the lottery? I would buy a house in Madrid. "Sonriera", in your sentence, is a subordinate of "hizo"( past of hacer), so, both, must be connected in tense, so, you can't use present simple. Pretérito Imperfecto del subjuntivo(Imperfect subjunctive), is a hard lesson for any Spanish teacher, even with spanish students. Your sentence could be in that way without any difference in meaning. Su juego de palabras aparentemente involuntario hizo al reportero "sonreir". I hope I have been helpful.

his words made the reporter smile