What do you call the words obtained by inversing the order of the sounds?

It is an example of Phonetic Reversal.
(or is it Phonemic reversal?, as Jon Purdy points out in the comments: reversal of the order of the phonemes /ch/, /ea/, and /t/ rather than the phones [t], [ʃ], [iː], and [t] or [ʔ]).

It could be an instance of backmasking, even though the Wikipedia article does mention:

Phonetic reversal is not entirely identical to backmasking, which is specifically the reversal of recorded sound.
This is because pronunciation in speech causes a reversed diphthong to sound different in either direction (e.g. eye [aɪ] becoming yah [jɑː]), or differently emphasize a consonant depending on where it lies in a word, hence creating an imperfect reversal.

Backmasking involves not only the reversal of the order of phonemes, but the reversal of the phonemes themselves, which means that the reversed sound of a phrase may be hard to predict.

So I am not sure that the word "teach" played reversed would actually gives "cheat".
If it doesn't, I didn't find any "one word" to characterize this particular inversion.

One or two, one, a Palindrome.

The palindromes could be a word or phrase which are read the same to one side or the other. In spanish is hard but not that much, remember that you say in spanish the same as you read, I mean:

Anilina - anilinA

Sometemos - sometemoS

Se es o no se es

In English:

Redivider - redivideR

God! a dog!

Never odd or even.

But in this case could be just the sound because, clearly teach - cheat are not written the same as for the palindromes, it should be:

teach - hcaet

Two, I think from what I've read that you could call it anagram, that's a rearranging of the letters of a word to form another:

Made - Dame

teach - cheat

And not as palindrome which should be JUST the inverse with no rearrange.

You could read about almost the same question here: Palindrome-anagram

Hope it helps.