yes that intuition is difficult. I have an attempt. So 1% of GDP is tradable. Also consumption and total production fixed. Mars cuts tax from t to 0. So to invest more Mars runs a current account deficit -- all cyberservice provided by earlhlings & martian cyberworkers go build capital. Note all the extra capital belongs to earthlings (I assumed martian savings are fixed).
In the long run, there will be current account balance. This means Mars will have a trade surplus required to pay the return on earthling owned capital on Mars. They owe us delta(k)r per year. They can run a trade surplus of only 1% of GDP so delta(k) less than or equal to 0.01 GDP/r
It seems to me the long run effect is entirely due to the fact that the tax cutting planet has to pay more capital income to the other one. This places a limit on the sum of their trade deficits and extra capital accumulation.
I think the limit on long run capital inflow is that hypothetical Mars (or the US in the real Solar system) can only owe the rest of the solar system liabilities which it can service. This is a long run limit -- a statement about the new steady state.
In the really real world, I think current US current account surplues are not sustainable forever, so the sum over the next century can't increase (or stay the same). So the long run effect of a profit tax cut is zero. But that's just a guess.