、。。
So, Reiko — you have no reason to panic.
Literal
Therefore, Reiko. You [topic-は] panic [nominalized-こと] [topic-は] does-not-exist.
~ことはない is a set grammar pattern 'there is no need to ~ / it's not necessary to ~' — not literally 'there is no ~ing.' アンタ is an informal, slightly rough variant of あなた, conveying familiarity mixed with a hint of condescension or exasperation depending on relationship. The mix of casual アンタ with polite ありません signals an older speaker reassuring a junior in a not-strictly-formal but still respectful tone.