how can i pass callback function parameters to the parent react component?

This appears to be a problem solved by Lifting State Up. useLazyQuery takes a gql query and options and returns a function to execute the query at a later time. Sounds like you want the child component to update the variables config parameter.

BrowseMovies

1. Move firstLetter state BrowseMovies component

2. Update query parameters/options/config from state

3. Add useEffect to trigger fetch when state updates

4. Pass firstLetter state and setFirstLetter state updater to child component

   const BrowseMovies = () => {
     const [firstLetter, setFirstLetter] = useState('');
   
     const [fetchMovies, { data, loading}] = useLazyQuery(
       BROWSE_MOVIES_BY_LETTER,
       { variables: { firstLetter } } // <-- pass firstLetter state
     );
   
     useEffect(() => {
       if (firstLetter) {
         fetchMovies(); // <-- invoke fetch on state update
       }
     }, [firstLetter]);
   
     return (
       <div className="browserWrapper">
         <h2>Browse Movies</h2>
         <AlphabetSelect 
           pushLetterToParent={setFirstLetter} // <-- pass state updater
           selectedLetter={firstLetter} // <-- pass state
         />
         {
           data && !loading &&
             data.browseMovies.map((movie: any, index: number) => {
               return (
                 <div key={index} className="browseRow">
                   <a className="movieTitle">
                     {movie.name}
                   </a>
                 </div>
               )
             })
         }
       </div>
     )
   }
   

AlphabetSelect

1. Attach pushLetterToParent callback to div‘s onClick handler

    const AlphabetSelect = ({ pushLetterToParent, selectedLetter }: any) => {
   
      const letters = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ#';
   
      return (
        <div className="alphabetSelect">
          {
            letters.split('').map((letter: string) => {
              return(
                <div
                  key={letter}
                  className={selectedLetter === letter ? 'letterSelectActive' : 'letterSelect'} 
                  onClick={() => pushLetterToParent(letter.toUpperCase())}
                >
                  {letter}
                </div>
              )
            })
          }
        </div>
      )
    }