Of course, there are two sentences there.

They are grammatical, but I may have written it as "that I hadn't checked up on you."

Context would tell you whether they were correct for your intended meaning. LIke "I already know" or "I knew already" may be more natural.

Here's the context. Please make me sure that it's grammatically correct.
Me:
I know about it. I was just pretending that I didn't check-up on you

Should I have read that from the bottom up?

me: Long-lost Scarlett! How have you been?
S: I'm okay. You?
me: I'm good. haven't seen you in ages. Why did you disappear like that? Do you still play?
S: Actually, I'm on vacation.
me: Yeah, I know, but I didn't want to make it look like I'm checking up on you.

(That is a little creepy - you may want to say something

Yea, read it from the bottom up.
I agree this sounds creepy so I will say what you have suggested me
I will say just say Yea, that's what I heard

BarbaraPAThey are grammatical, but I may have written it as "that I hadn't checked up on you."

Oh Barb.You've gone over to the other side.

What do you mean? Is there an error in my version?
And is there better ice cream on this side?

I am old, school.

If I know I didn't do something, I may/ might have done it (had circumstances been different).
If there is a possibility that I did it, I may/might have done it.

Fred said no. I may/might have said yes, but nobody asked me.
I may/might have said yes; I can't remember.

Ah, thanks.
I don't think Americans differentiate between may and might much. But your examples are helpful in showing the perceived differences.

Actually, I don't think many speakers of BrE differentiate much between the two in the non-perfect forms.

With a sentence such as I may/might see him tomorrow, I don't think many feel nowadays that might is more uncertain than may.

In conditional sentences, might and may are now acceptable in the first, but only may works in the second (