When conducting a two-tailed z test with a = 0.01, the test value was computed to be 2.07. the decision would be to reject or to not reject the null hypothesis

You reject the Null Hypothesis only if the p-value is less than alpha.
p < 0.01

To find the p-value, you need to look up test value 2.07 in a standard normal table. The p-value is probability that Z > 2.07. For a two-tailed test, you include both positive and negative cases. |Z| > 2.07.

When you look up 2.07 you get about 0.98.
This means there is about 2% chance Z > 2.07 or 4% chance |Z| > 2.07.

For the two-tailed test we use p = 0.04
.04 > .01
Therefore we do Not reject the Null Hypothesis.