Just to be clear, here's the paragraph from Nocedal and Wright that I'm copypasting from a comment on a different thread.  I don't know anything about this parameter other than what is written in this paragraph.
```
"The choice of the tolerance epsilon_k at each call to Algorithm 7.2 is important
in keeping the overall cost of the trust-region Newton-CG method low.
Near a well-behaved solution x_star, the trust-region bound becomes inactive,
and the method reduces to the inexact Newton method analyzed
in Theorems 7.1 and 7.2.  Rapid convergence can be obtained in these circumstances
by choosing epsilon_k in a similar fashion to Algorithm 7.1."
```