I didn't really catch what he said, but I answered him anyway.
I didn't really understand what he said to me, so I just gave him an arbitrary answer.
この場合、次のような言い方ができますよ。
ーI didn't really catch what he said, but I answered him anyway.
「彼の言ったことを聞き取れなかったけど、いい加減に答えておいた」
anyway で「いい加減に・ぞんざいに」
ーI didn't really understand what he said to me, so I just gave him an arbitrary answer.
「彼の言ったことが理解できなかったので、思うままに答えておいた」
arbitrary で「恣意的な・気ままな」
ご参考まで！
カナダ 
