The seed is only displayed on your Trezor screen, for you to write down. It is also only displayed once.
Trezor Suite does not know your seed.
The “Check seed” feature only works in combination with your Trezor. You enter the seed, as if you were recovering it, and Trezor tells you “this was the right seed” or “this was not the right seed”
On Trezor One, you have the option to check the seed by typing words, in scrambled order, into the PC. In this case, the Suite can see the words, but doesn’t know the correct order – and the number of possibilities is large enough that it can’t be brute-forced to get the right one.
Of course, Suite does not save the words.
Trezor screen will tell you in what order you enter the words. Sometimes it will also insert a decoy word: the Trezor screen says “now type the 3rd word; now type the word ‘abandon’”. Suite does not know if the word is a decoy or not.
The alternative option is to type words using a matrix, similar to PIN. In that case, Suite only sees the clicks, and only the Trezor screen knows what you’re clicking.