It's much easier to use the "Rods from God" idea - that is more precise and minimizes collateral damage.
IRL you can use brain-power to avoid using muscle-power!
On the other hand, in-universe, they've got brute-force Epstein drives. For them this is Tuesday.
From https://www.britannica.com/science/Earth-impact-hazard/Frequ...:
> Because there are far fewer large NEOs and long-period comets in space than smaller ones, the chances of a collision decrease rapidly with increasing size. The impact-hazard community—primarily scientists with an interest in the issue—has defined a global catastrophe to be an impact that leads to the death of one-fourth or more of the world’s population. An impact by a 1-km- (0.6-mile-) diameter NEO, the smallest believed capable of causing such a catastrophe, is estimated to occur about once per 100,000 years on average, based on the assumed population in space of such objects. On the other hand, an impact by a 100-metre (328-foot) NEO, the smallest believed capable of causing regional devastation, is estimated to occur about once every 1,000 years on average.
Take your pick!
And remember one doesn't need a tidy Hohman transfer. Rather the opposite in fact. The nastier the intersect angle the better.
(Hopefully we don't end up on some watchlist :-P )
INSTABANG!1!!