After each guess, the player is told whether each individual letter in that position in the word is earlier or later in the alphabet than the guessed letter.

After three guesses she knew the first letter was C-H, the second A-H, the third E-R, the fourth A-D and the final letter U-Z. DELAY obviously fits this, along with some other possibilities such as FANCY, which I hid in plain sight in the question.

I based this puzzle on the game ‘Wordle Peaks’ which I play every day. You can find it at: https://vegeta897.github.io/word-peaks/