レシート is supposed to mean receipt. The adaptation of the word looks a bit odd to me. If it comes from English, why does it lose the "p"? Why it uses a "shii" sound instead of a "ce" (to me there are katakana characters which sounds more similar to "ce" than "シー"? Maybe it comes from another language than English where the word is more similar to the sound レシート? Which is it?
Derivation of レシート
Numerous dictionaries state that レシート is from English receipt. See, for instance, the Dajisen and Daijirin entries visible here at Kotobank (in Japanese), or here at Wiktionary (in English; full disclosure: I edited that entry. See the listed sources there for authoritatively edited materials.).
Why it is rendered this way in Japanese
The English term receipt is pronounced by all native speakers I personally know as something like [[ɹɪˈsiːt]] or [[ɹɛˈsiːt]]. For instance, the ⟨p⟩ in the spelling is not pronounced. Separately, the ⟨ce⟩ in the spelling combines with the ⟨i⟩ to be pronounced as //siː//, not as //seː// nor //ceː// -- the same as in receive.
The Japanese katakana rendering is thus a close approximation of the English pronunciation, ignoring the oddities of the spelling.
For more about the English term, including the pronunciation and a description for where that unpronounced ⟨p⟩ came from, see the Wiktionary entry for receipt.
There isn't a one-to-one mapping of Latin-based alphabets to the Japanese writing system. So to answer your question:
'why does it lose the "p"?'
Katakana is syllabic - so when a foreign / loan word is written is Japanese, they typically use the sound of the word (any "spelling" similarity is purely coincidental). This applies to any English word with silent letters, as they will not appear in the phonetic rendering of the word.
When we say receipt in English, phonetically we sound identical to the English word "reseat" too. Sounding something like:
One aspect / limitation of Japanese is its pronunciation rules - it has a finite list of syllables / Kana to choose from. The "see" sound in the middle of "receipt" is one such absence.
So, in Japanese we end up with (using the Hepburn romanization system):
レ (re) シー (shi) ト (to)
Hepburn (and other systems) standardise the way we spell Japanese syllables. So シ (shi) is pronounced similarly to the English pronoun "she", with a long vowel. English spelling is notoriously inconsistent:
"I did some reading in Reading." etc.
A consequence of having a consistent romanisation system (spelling of syllables) is that it highlights this inconsistency.