This is a good poem (previously Reject Note)

[Richard]

Hey ritwiksadhu33,
I like some of the images you use here. I'll go into more detail below:

Reject Note -May be it should read "Rejection Note"? I'm not a huge fan of this title because I find you stray a bit from this image.

This is a good poem. -This line is dangerous because it would be an easy line to mock if this poem was terrible, which it is not. My thinking is that you might as well go all in on this line and make it the title.

It speaks sparingly,
and only on matters of great import,
with well chosen words.
It doesn't carry over, or under. -I get what you're going for here. However, if you want to keep these images in the poem, I would suggest expanding on them because it feels like you're just scratching the surface here.
You relate to it on a subconscious level.
Your subconscious relates to it on a subconscious level. -The repetition of "subconscious" is a bit excessive, and I find it creates almost a comedic effect that isn't consistent with the rest of the poem. 
It comes from a good family. -I quite like this line and the rest of the family imagery/metaphor. My suggestion would be to cut the first six lines of the poem and start here. If you changed the title to "This is a good poem", I think starting here would make sense.
An obedient son, caring parent,
loving husband. Or at least dutiful.
Somewhat conservative on social issues.
Has an affable old guy sort of personality.
The instant you see it you start getting good vibes.
It says “thank you” when you offer it tea,
and accepts the proffered cup gingerly,
sippping without a sound - most British. -Perhaps it should make a sound because sound is a big part of poetry.
It inclines its head as it passes you on the street,
acknowledging your existence, but not
enjambing over your awkwardness.
It realizes you don't want details. -I would end the poem here, or keep going with the idea of details the poem has to communicate even though it knows most people don't want them.
It pats your dog on the head, calls him “a good boy”.
For an instant you think it is talking about you.

Is it publication material?
Maybe but not sure.
It hopes to talk to me sometime later.
Encourage the author to submit again. -Personally, I don't find that this goes with the previous stanza, and if not for the title, it would feel really out of place. That is why I would recommend cutting this stanza.

I think you have a good first draft here, and I hope some of what I said helps you move in the direction you want.

Cheers,
Richard