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let newArray = [];
for(let i = 0; i < allItems.length; i++){
    let item = allItems[i];
    if(item.value == 'hi' || item.value.indexOf('h') > -1){
        // add to new array.
        newArray.push(item.id);
        // Or store the whole object:
        newArray.push(item);
    }
}

This is fairly basic stuff when working with arrays in javascript. What did you try before this?

Also, in my opinion, you definitely don't need a library to do this.