Hi @jeniviya ,
Do you want the nested gallery will only related items based on the item value in gallery1?
If so, I think you should Ungroup the table firstly. Or else, the gallery2 could only filter correctly.
I've made a similar test for your reference:
1)gallery1's Items:
Distinct(Ungroup(test4,"test"),field2)
2)gallery2's Items:
Filter(Ungroup(test4,"test"),field2=Subtitle2.Text)
Then gallery2 will only display the related items of the outside item.
(test4's stucture:
ClearCollect(test1,{field1:"a",field2:"aa",field3:"111"},{field1:"b",field2:"bb",field3:"222"},{field1:"c",field2:"cc",field3:"333"},{field1:"a",field2:"bb",field3:"111"});ClearCollect(test4,GroupBy(test1,"field1","test"))
)

On your side, you should try:
gallery1's Items:
Distinct(Ungroup('QC Check Lists',"'Check List Group'"),'Check List Group Name')
gallery2's Items:
Filter(Ungroup('QC Check Lists',"'Check List Group'"),'Check List Group Name'=Title1.Text)
If my understanding is incorrect, please describe more clearly about the feather that you want and show me the structure of your collection.
Best regards,