If someone pronounces "pizza" as /piːzə/ instead of /pitsə/, we'd surely raise an eyebrow at them. But few people (that I know personally) mind when we pronounce "tagliatelle" with a hard G (I wasn't even aware that this was 'incorrect' until recently.)
So the question is: are there consistent and observable processes that happen when we borrow loanwords into another language? Or is the process of change seemingly arbitrary? I imagine there must be some cultural differences involved, seeing as Americans often use a more native pronunciation of words like "fillet" /fɪleɪ/ whereas Brits say /fɪlɪt/. But other than that, I don't know why it is we keep some features of the native pronunciation (like the /ts/ in pizza) and lose others.