The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 letter word TAKE THE CAKE
I've seen this crossword clue in The Times
T
A
K
E
T
H
E
C
A
K
E
More clues leading to the result TAKE THE CAKE
Buddy explains!
The straight part
We know that "Children given doggy-bags at party may/be most remarkable?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case children given doggy-bags at party may/be most remarkable? = take the cake.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.