G mixolydian in my opinion, whoevver notated that score is not quite right either because i think NO KEY SIGNATURES should be used for G mixolydian the scale: G , A , B , C , D , E , F♮( NOT F♯)by RC2630 - Music Theory Questions and Answers
for say chord I is B♭major and chord vii is A minor meaning guaranteed B♭& guaranteed E♮. given this information, we think that F major has B♭but no E♭, instead having E♮. We observe that the equivalence of F major starting on 4^ is B♭lydian. now, here is a summary of all 7 diatonic chords of B♭lydian - found from I to vii: I - B♭major - B♭, D , F II - C major - C , E , G iii - Dby RC2630 - Music Theory Questions and Answers