Reibun
。。

She's a genuine well-bred lady, you know. Unfortunately, that's not a prank or anything — that's just how she naturally is.

Literal

Pure-blooded [attributive-の] young-lady is-[because-だから][emphatic-な]. Unfortunately prank [and-such-とか][is-not-じゃなくて] that [with-で] natural is-[copula-だ].

生粋 ('pure-bred, unadulterated') is a formal adjective used for lineage or authenticity of character — 生粋の江戸っ子 'a true Edoite.' お嬢様 is a social category: the daughter of a well-to-do family, stereotyped as refined, sheltered, and somewhat otherworldly in manner — a staple fiction archetype. 素 here means 'one's natural state / true self' (vs. an act or performance). あれで素 'that's her being natural' — で is the copula te-form in its means/manner sense.