There are some examples of "what it".
Barely I can hear clearly the connective of the two words.
When a word ending with a consonant is followed by a word starting with a vowel, the two words are run together, so what it -> whatit. The speaker in the recording is American: when a t occurs between two vowels, American speakers pronounce it as an alveolar flap, which sounds like a d. You can hear that happening with the t at the end of what.
The word it is unstressed, so the i is shorter and softens to a schwa /ə/.
American English has the tendency to delete a schwa when it appears in a midword syllable that comes after the stressed syllable. Kenstowicz (1994) states, "American English schwa deletes in medial posttonic syllables". He gives as examples words such as sep(a)rate (as an adjective), choc(o)late, cam(e)ra and elab(o)rate (as an adjective), where the schwa (represented by the letters in parentheses) has a tendency to be deleted.
Final t's are rarely strong, especially in an unstressed syllable.
To sum up, the it is there, but it is shorter and gentler than a non-native listener might expect. American English listeners (and British English listeners who watch a lot of American movies) expect it to be weak in this context, so they can hear it clearly.