La compagnia assicurativa rimborsa la spesa.

Because rimborsa is the conjugated verb, while rimborsare is the infinitive.

• rimborsare = to reimburse
• rimborsa = he/she/it reimburses

In this sentence, the subject is la compagnia assicurativa, which is grammatically third person singular, so the verb must be rimborsa.

Because both nouns are feminine singular, and in Italian they normally take an article.

• la compagnia = the company
• la spesa = the expense / the cost

Italian uses definite articles more often than English does, so keeping la in both places is completely normal.

Because assicurativa is an adjective describing compagnia, and adjectives in Italian usually agree with the noun in gender and number.

• compagnia is feminine singular
• so the adjective must also be feminine singular: assicurativa

Compare:

• una compagnia assicurativa = an insurance company
• un settore assicurativo = an insurance sector

They are very similar, and both can mean insurance company.

• compagnia assicurativa uses an adjective
• compagnia di assicurazione uses a noun phrase, literally company of insurance

Both are natural Italian. Compagnia assicurativa is compact and very common; compagnia di assicurazione is also standard and may sound slightly more explicit to learners.

Here, spesa means expense, cost, or amount spent.

It is a very common word in Italian, but it has more than one use depending on context:

• la spesa = the expense / the cost
• fare la spesa = to do the shopping / buy groceries

In this sentence, it clearly means the expense being reimbursed.

Because rimborsare can take a direct object in Italian.

So Italian says:

• rimborsare la spesa = reimburse the expense

English often uses structures like reimburse the expense or pay back the cost, so this direct-object pattern is not strange in Italian.

You can also have a person involved:

• La compagnia assicurativa rimborsa la spesa al cliente. = The insurance company reimburses the expense to the customer.

Here:

• la spesa = direct object
• al cliente = indirect object

No, that would sound wrong in standard Italian.

You normally need the article here because you are talking about a specific expense or a specific category of expense:

• rimborsa la spesa = correct
• rimborsa spesa = incorrect in normal Italian

Italian articles are often required in places where English might not use one.

The standard order here is:

• La compagnia assicurativa = subject
• rimborsa = verb
• la spesa = object

So the sentence follows a normal subject–verb–object pattern.

You can change the word order in some contexts, but it usually changes the emphasis:

• La compagnia assicurativa rimborsa la spesa.
  Neutral, standard.
• La spesa la rimborsa la compagnia assicurativa.
  Emphasizes the expense.
• Rimborsa la spesa la compagnia assicurativa.
  Possible, but less neutral and more context-dependent.

For a learner, the original order is the safest and most natural.

A few parts are especially important:

• gn in compagnia is like the ny sound in canyon
• the stress is on -gnì-: com-pa-gnì-a

A rough guide for an English speaker is:

• com-pah-NYEE-ah

Also:

• assicurativa has a clear double ss
• rimborsa has a rolled or tapped Italian r
• spesa is pronounced SPAY-zah in standard Italian

It is in the present tense, and in Italian the present can express different ideas depending on context, including:

• something happening now
• a general fact
• something that happens regularly

So La compagnia assicurativa rimborsa la spesa could mean:

• The insurance company is reimbursing the expense
• The insurance company reimburses the expense
• The insurance company does reimburse the expense

Without more context, the sentence is simply a neutral present-tense statement.

Sometimes, but not always.

• spesa usually refers to an expense or money spent
• costo usually refers to the cost/price of something

So:

• rimborsare la spesa is very natural
• rimborsare il costo is possible in some contexts, but it can sound more limited or specific

If you mean an expense someone paid, spesa is often the better choice.