Just to expand on the answer by @Siv:
Previous studies have indeed suggested teleconnections between the jet stream and ENSO (for example: Horel 1981). Recall that, at a fundamental level, the jet stream (a westerly geostrophic wind pattern) is driven by horizontal North-South temperature gradients across cold and warm air masses (thermal wind). Thus, it can be enhanced by increasing the temperature gradient of the two air masses.
Because winter frontal zones have characteristically larger temperature gradients than summer fronts, the jet stream is strongest during the boreal winter. It also moves equatorward to $30^o$ from its typical position in the summer of $50-60^o$.
And as discussed in Chunzai Wang, 2002:
During El Niño–La Niña events, the atmospheric westerly jet stream
tends to move meridionally [...] El Niño (La Niña)
corresponds to westerly (easterly) wind anomalies in the upper
troposphere of the midlatitude Pacific, associated with the
equatorward (poleward) displacement of the jet stream.
So, the enhancement/reduction is due to the displacement of the jetstream and associated increase/decrease in the temperature gradient across the cold/warm air masses that are generating the jet stream in the first place.
Horel, J. D., and J. M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev, 109, 813–829.
Chunzai Wang, 2002: Atmospheric Circulation Cells Associated with the El Niño–Southern Oscillation. J. Climate, 15, 399–419