How do I extract specific lines based on a comparison of two files with sed and/or awk?

I need to extract all the lines from file2.txt that do not match the string until the first dot in any line in file1.txt. I am interested in a solution that stays as close to my current approach as possible so it is easy for me to understand, and uses only sed and/or awk in linux bash.

file1.h

apple.sweet banana
apple.tasty banana
apple.brown banana
orange_mvp.rainy day.here
orange_mvp.ear nose.png
lemon_mvp.ear ring
tarte_mvp_rainy day.here

file2.h

orange_mvp
lemon_mvp
lemon_mvp
tarte_mvp
cake_mvp

result desired

tarte_mvp
cake_mvp

current wrong approach

$ awk '
    NR==FNR { sub(/mvp(\..*)$/,""); a[$0]; next }
            { f=$0; sub(/mvp(\..*)$/,"", f) }
    !(f in a)
' file2.h file1.h

apple.sweet banana
apple.tasty banana
apple.brown banana
orange_mvp.rainy day.here
orange_mvp.ear nose.png
lemon_mvp.ear ring
tarte_mvp_rainy day.here

>Solution :

Using awk

$ awk -F. 'NR==FNR {a[$1]=$1;next} a[$1] != $0' file1.h file2.h
tarte_mvp
cake_mvp