He must know, then, she thought. Someone at the co-op has told him.
The two marked sentences are both direct "speech", although Oates does not mark them with quotation marks—probably because they are not spoken but only thought. The must here therefore represents present tense.
But the past tense of must is not had to, though had to may substitute for it. The past tense of must is must†.
In any case, there is no justification for using either may or might here; either would completely change the meaning.
† Historically, in fact, must was the past tense of the verb mote, which long since disappeared from use. Must appears to be following in its footsteps, being more and more replaced by the more flexible quasi-modal HAVE to.
Correct answer is most likely, "She asked me if I love her." but the other one is ok.
I think you missed the important part. What's the correct answer to say back to her? The woman talks in code. The answer to "Do you love me?" is very difficult and advanced. It all depends on which word is stressed, which indicates uneasiness or doubt.
Her: "Do you love me?" Then she has doubts about the honest of your love. Maybe your capability.
Correct Answer: "Of course I love you. If I didn't love you, I would have been gone a long time ago. I'll always love you."
But they get harder....
Her: "Do you love me?" Then she has doubts about the you loving her.
Correct Answer: "I love you like I've nover loved anyone in my life. Yes I love you!"
Her: "Buy why do you love me?"
You: "Because your special. You're kind. You love people. You're the best girl I've ever met. You're beautiful on the inside and out. You drive me crazy!"
Her: "Do you love me?" Then she doubt about your love for her.
Correct Answer: "I always love you. My heart is yours forever. I've never stopped and I never will."
Her: "Then why didn't you do X" where "X" is something you never would have thought doing, like stacking her dishes to the left.
You: "Because I wanted to make you mad."
Her: "Whaaat?"
You" "I'm joooking! I didn't know that was important. You know I try to be a mindreader. I'm just not good enough at it yet. I want more practice. My energies say you want a shoulder rub right now."
Her: "That's not what I was thinking..."
You: "I know what your mind was thinking, But your body was screaming for a shoulder rub..."
Her: "Do you love me? Then she has some doubt or insecurity about herself.
Correct Answer: "Yes I love you. You're the only one I love. I love everything about you. I love your eyes, your smile, your face, you laugh. But most of all, I - LOVE - YOU!"
Her: "Then what about that girl you were talking to?"
You: "Which one? I talk to so many..." She hits you playfully. "Owww!" you say with more pain and flinching that it really hurt. "Don't be so jealous/silly/whatever, I was asking her what I should get you for a present."
Best Answer
TO LET is not a modal verb. It is different from them semantically and formally.
A speaker or writer can express certainty, possibility, willingness, obligation, necessity and ability by using modal words and expressions.
Speakers often have different opinions about the same thing.
Modal verbs
Here are the main verbs we use to express modal meanings:
Core modal verbs: can, could, may, might, will, shall, would, should, must.
Semi-modals: dare, need, ought to, used to.
Other verbs with modal meanings: have (got) to, be going to and be able to." (https://dictionary.cambridge.org/grammar/british-grammar/modals-and-modality/modality-introduction)
TO LET is an action verb. It means 'to allow'. It is also used as a polite way of making or responding to a suggestion, giving an instruction, or introducing a remark.
// Could you let the dog out?
// Let's have a drink!
// They've let out their house.
// A tiny window that let in hardly any light.