High-energy proton-proton (pp) collisions at large final state particle multiplicities exhibit heavy ion-like behaviors. Among many others, one of the peculiar feature of heavy ions is partonic energy loss (aka jet quenching) in the produced Quark-Gluon Plasma. The search for jet quenching effects also in small collision systems (such as pp) is warranted. To date no evidence of jet quenching has been observed in pp collisions. The presented work aims to contribute to these searches by studying possible event selection biases which may distort the observed effects measured in pp collisions, and this way can affect the interpretation of observables used to study jet-quenching. Two-particle angular correlations are used in simulated events by the PYTHIA 8 Monte Carlo model to investigate the unavoidable underlying event (UE) background and the consequence of the increased number of multiple parton interactions, which cause the signal distribution to be distorted. A stategy for the modelling and subtraction of the UE is discussed. We found that the signal in the away region of the azimuthal correlation is less affected by biases and more suitable to examine in experimental measurements.