A recent ALICE measurement reports a finite strangeness enhancement in the toward-leading region of high-multiplicity proton-proton collisions. In this work, the trigger transverse momentum, , dependence is investigated using and production in PYTHIA8, with and without color ropes, and EPOS-LHC. For ~GeV/, EPOS-LHC and PYTHIA8 with color ropes exhibit a multiplicity-dependent increase of the toward-leading ratio, while the rope-free PYTHIA8 baseline shows a weaker dependence. With increasing trigger momentum, the enhancement is strongly suppressed in EPOS-LHC for ~GeV/, whereas it remains approximately unchanged in PYTHIA8 with color ropes. This contrasting behavior is consistent with a reduced core contribution in EPOS-LHC and a local string-overlap mechanism in PYTHIA8 with color ropes. The trigger transverse momentum thus provides a model-sensitive probe of the mechanisms contributing to the apparent strangeness enhancement in the jet-like region of the pp collisions.

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