Magnetosheath jets are dynamic pressure enhancements observed in the terrestrial magnetosheath. Their generation mechanisms are currently debated but can be linked to foreshock processes. Recent results showed that jets are less numerous when coronal mass ejections (CME) cross the magnetosheath. Here, we show for the first time how CMEs and their magnetic ejecta (ME) region are related to jet production. Based on THEMIS and OMNI data covering 2008–2021, we show the probability distribution of jet production in 2D parameter histograms using the IMF cone angle and Alfvén Mach number. We compare this distribution with the values within CME-MEs. We find high cone angles and low Alfvén Mach numbers within CME-MEs, which both are unfavorable for jet production as they may inhibit a proper foreshock region. We predict that future missions, measuring the magnetosheath of Mercury, will find low numbers of jets due to low Alfvén Mach numbers.