Vânzătoarea nu rambursează banii fără să verifice dovada achiziției.

Because vânzătoarea means the saleswoman.

• vânzătoare = saleswoman / female seller
• vânzătoarea = the saleswoman

In Romanian, the definite article is usually attached to the end of the noun, not written as a separate word like English the.

That is the normal way to negate a verb in Romanian.

• rambursează = refunds
• nu rambursează = does not refund / doesn’t refund

Romanian usually puts nu directly before the finite verb.

Yes. rambursează is the 3rd person singular present tense of a rambursa.

Here, the present tense expresses a general rule, habit, or policy, not just something happening right now. So the sentence sounds like a store policy or regular practice:

• The saleswoman doesn’t refund the money without checking the proof of purchase.

In Romanian, bani is commonly used as a plural noun meaning money.

• bani = money
• banii = the money

So even though English usually treats money as singular, Romanian often uses this plural form. That is completely normal.

fără să + verb is a very common Romanian structure meaning without doing something.

So:

• fără = without
• să verifice = (that) she check / checking in this structure
• fără să verifice = without checking

English often uses without + -ing, but Romanian typically uses fără să + subjunctive.

Because after să, Romanian usually uses the subjunctive form, not the normal indicative present.

Compare:

• verifică = she checks / is checking
• să verifice = subjunctive form, used after words like să

So after fără să, the correct form here is verifice.

It is still vânzătoarea.

Romanian often leaves out subject pronouns when the subject is clear from the context. So there is no need to say ea (she) here.

The understood meaning is:

• The saleswoman doesn’t refund the money without checking the proof of purchase.

No. It is not a double negative in the English sense.

The idea is:

• she does not refund the money unless she checks the proof of purchase

So the sentence means that checking is required before the refund happens.

A natural English interpretation is:

• She doesn’t refund the money without checking the proof of purchase
• or more idiomatically, She won’t refund the money unless she checks the proof of purchase

This is a noun phrase meaning the proof of the purchase or proof of purchase.

• dovada = the proof
• achiziției = of the purchase

Here achiziției is in the genitive case, because it depends on dovada: proof of purchase.

Base noun:

• achiziție = purchase
• achiziției = of the purchase / to the purchase depending on context

In this sentence, it is clearly genitive: proof of purchase.

Yes. Both are possible.

• fără să verifice
• fără a verifica

Both can mean without checking.

The version with fără să is very common and natural in everyday Romanian.
The version with fără a + infinitive can sound a bit more formal or written.

Yes, it is a correct and common verb, especially in more formal, business, or customer-service contexts.

• a rambursa = to refund / reimburse
• rambursează banii = refunds the money

Depending on context, Romanian may also use other verbs, but a rambursa fits this sentence very well because it focuses on giving the money back.