Ah, got it. Because of the vowel beginning ils, you say the final t in veulent (but not the s in ils; I don't know why) - so it's like 'veul-t il une chemise'. But when you slur it together at speed it sounds like 'veul tilune chemise'.
To me, that t sounds like the ts in 'tsunami', and I think it's fair enough if they don't make a clear and precise 't' sound. After all, in English I can say 'they wanna'.
I don't have problem with the "t" but I really couldn't hear the "veu" sound (I heard something like "daw/dor" or "paw/por" sound). May be I'm half-deaf
because "ils" is plural, so the verb is conjugated for 3rd person plural
Because (I think) the "l" in "veulent" is pronounced and therefore it can be differentiated from "veut" (not homophones).
I'm sure that this has been asked before, but how can you tell the difference between il/elle and ils/elles?
In this sentence, you have to look at the verb: "veulent" is 3rd person plural (ils/elles) while "veut" would be 3rd person singular (il/elle).
Inversions of the interrogative form are always built in a way that the pronounciation is eased. Hence, the addition of a consonant sound between vowel sounds, in order to ensure a better flow of sounds than if it were "VEUL-IL".
"Would like" is conditional mode, translating to: "voudraient-ils une chemise ?"