She decorated the house regardless of cost.

Literal

She [topic-は] expenses [object-を] regardless decorated-up.

費用を顧みず ('regardless of cost') uses 顧みる (かえりみる, 'to consider/look back at') in its ず-form (classical negative adverbial). 飾りたてる means 'to decorate lavishly' — a compound of 飾る ('decorate') + 立てる (intensifier).