Potentiometer as variable resistor
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) The original circuit. (b) The alternate circuit. Both ignore the non-inverting offset reference for simplicity.

In Figure 1a the gain can be adjusted from \$ - \frac {10k} {20k} \$ to \$ - \frac {10k}{30k} \$, -0.5 to -0.33. It is common to connect the wiper to one end of the pot so that if there's a bad spot on the track that a completely open circuit is avoided. 

In Figure 1b the overall circuit gain can be adjusted by R6 from 0 (wiper at bottom) to -0.5 (wiper at top).

Which is better is up to you.