Por mucho que valoremos su carta de presentación, la revisamos.

Por mucho que is a concessive expression. It means something like:

• no matter how much
• however much
• even though ... very much

It introduces an idea that does not change the result in the main clause.

So the structure is:

• Por mucho que + subjunctive, main clause

In this sentence, the idea is: even if we value the cover letter a lot, we still review it.

Because por mucho que normally triggers the subjunctive.

Spanish uses the subjunctive here because the speaker is not stating a simple fact in a neutral way; they are presenting a concession: regardless of how much we may value it.

So:

• valoremos = present subjunctive, nosotros form of valorar
• infinitive: valorar
• indicative would be valoramos
• subjunctive here: valoremos

This is very common after expressions like:

• por mucho que
• aunque sometimes
• por más que

Because the main clause is presented as a real statement or fact.

• Por mucho que valoremos... = concessive idea, so subjunctive
• la revisamos = what we actually do, so indicative

This contrast is very typical in Spanish:

• subordinate concessive clause -> often subjunctive
• main statement -> indicative

So the sentence mixes moods for a reason: the first part is the concession, the second part is the actual result.

Valoremos is the present subjunctive of valorar in the we form.

Full present subjunctive of valorar:

• yo valore
• tú valores
• él/ella/usted valore
• nosotros/nosotras valoremos
• vosotros/vosotras valoréis
• ellos/ellas/ustedes valoren

In this sentence, valoremos means we value / we may value in a subjunctive sense.

La refers to su carta de presentación.

Since carta is feminine singular, the pronoun is la.

So:

• su carta de presentación -> feminine singular noun phrase
• la revisamos -> we review it

Spanish often uses an object pronoun instead of repeating the whole noun:

• Revisamos su carta de presentación
• Su carta de presentación, la revisamos

Here the pronoun avoids repetition and links directly back to the letter.

Because su + noun is the normal and most natural way to say your / his / her / their before a noun.

So:

• su carta de presentación = the usual phrasing

You can say la carta de presentación suya, but that is less neutral and often used for emphasis, contrast, or disambiguation.

For example:

• Revisamos su carta de presentación = neutral
• Revisamos la carta de presentación suya, no la de otra persona = more emphatic/contrastive

It can mean any of those, depending on context.

Su can refer to:

• your (formal singular)
• his
• her
• its
• their
• your (plural, in many contexts)

In this sentence, because carta de presentación is a job-application phrase, su will very likely mean your in a formal, polite sense.

In Spain, if you were speaking informally to more than one person, you would usually say vuestra carta de presentación, not su carta de presentación.

Not usually in the English sense of rewrite/edit.

Spanish revisar often means:

• to review
• to check
• to look over
• to inspect

So la revisamos here is more naturally understood as:

• we review it
• we check it

This is an important false-friend point: English revise often means study again or rewrite, but Spanish revisar usually means check/review.

Because the sentence begins with a subordinate concessive clause:

• Por mucho que valoremos su carta de presentación, ...

After that introductory clause, Spanish normally places a comma before the main clause:

• ..., la revisamos

This works much like English punctuation with introductory clauses.

Yes, you could say that, but it is not exactly the same in emphasis.

Compare:

• Aunque valoremos mucho su carta de presentación...
• Por mucho que valoremos su carta de presentación...

Both can mean something like even though / no matter how much we value your cover letter, but por mucho que puts stronger focus on the degree:

• however much
• no matter how much

So por mucho que sounds more emphatic.

It is grammatically correct, but by itself it can sound a little unusual or incomplete in logic.

That is because por mucho que often introduces a stronger contrast, and many speakers might expect something like:

• Por mucho que valoremos su carta de presentación, tenemos que revisarla igualmente.
• Por mucho que valoremos su carta de presentación, no podemos aceptarla sin revisarla.

Your original sentence is still understandable, but many learners may feel it sounds slightly odd because we value it a lot, so we review it is not a very strong contrast on its own. Usually por mucho que works best when the second clause clearly shows despite that.

Yes, but the original order is useful because it foregrounds the concession.

Original:

• Por mucho que valoremos su carta de presentación, la revisamos.

Possible alternative:

• La revisamos, por mucho que valoremos su carta de presentación.

The original is more natural if you want to start with the idea no matter how much we value it.

Spanish often places this kind of concessive clause first for emphasis.