How do we obtain this inequality? A question concerning an argument in Ethier and Kurtz 1986 (pg 137))

Question

In page 137 of Ethier and Kurtz(1986 - Markov processes, convergence and characterization) one reads:

I don't see how that follows, imagine that $\Delta >\delta$ so $q(X(\delta), X(\Delta \wedge \delta)) = 0$ and if (8.27) were true then

$$q^{2\beta}(X(\delta), X(0))\leq a_\beta q^\beta(X(\delta), X(0)) $$ and suffices to take $q(X(\delta), X(0)) > a_\beta$ to see that this inequality doe not hold. (Or am I making a mistake)

If there is indeed a typo here, then how would one proceed with the proof of the result (8.18)?

Here below are some of the objects that come into play:

and

Please let me know if you need any further description.