Defeated creatures to the discard pile...

[the JabberwocK]

The Lidless Eye Rulebook states:

MARSHALLING POINTS
You only receive kill marshalling points for defeating a creature with an * next to its marshalling points. You may use
the creature's card as a trophy card (see below) or you may place the card in your marshalling point pile.
Note: A Wizard player does not receive marshalling points for defeating such a creature with an * next to its
marshalling points.
If you defeat a creature that does not have an * next to its marshalling points, you may use the creature's card as a
trophy card (see below) or you may place the card in your out-of-play pile. You do not receive marshalling points for
defeating it.
Note: You do not receive marshalling points if the creature you defeat is one of your own cards.

Does the use of the word may mean the resource player could opt to have the creature go to his opponent's discard pile instead of placing the card in his out-of-play pile? Or is the resource player required to place the card in his out-of-play pile if he is unable or unwilling to take the creature as a trophy or put in MP pile?

[Konrad Klar]

Taking a trophy is an option.

[CDavis7M]

For example, a lone Ring wraith defeats a creature but the RW cannot take a trophy. But, it is a non * creature so it doesn't go into the MP pile. Where does the creature go?

Seems like removing it from the game is the answer. But MAYbe it could be discarded.

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[Konrad Klar]

Where does the creature go?

To a MP pile or to a out-of-play pile.