Despite limiting access to applicants from underrepresented racial and ethnic groups, the practice of using hard or soft GRE cut-off scores in physics graduate program admissions is still a popular method for reducing the pool of applicants. The present study considers whether the undergraduate institutions of applicants have any influence on the admissions process by modelling a physics GRE cut-off score with application data from admissions offices of five universities. Two distinct approaches based on inferential and predictive modelling are conducted. While there is some disagreement regarding the relative importance between features, the two approaches largely agree that including institutional information significantly aids the analysis. Both models identify cases where the institutional effects are comparable to factors of known importance such as gender and undergraduate GPA. As the results are stable across many cut-off scores, we advocate against the practice of employing physics GRE cut-off scores in admissions.