En lo que respecta a la integridad, la comprobamos.

It means as for, regarding, with regard to, or as far as ... is concerned.

So:

• En lo que respecta a la integridad = As for integrity / Regarding integrity

It is a fairly formal way to introduce a topic.

No. In this expression, respecta a does not mean shows respect to.

Here, respectar is being used in the sense of:

• to concern
• to relate to
• to have to do with

So En lo que respecta a la integridad is basically When it comes to integrity or As far as integrity is concerned.

Here lo que is a fixed structure meaning something like that which or what.

A very literal breakdown would be:

• en = in / on
• lo que = that which / what
• respecta a = concerns / relates to

So the whole phrase is idiomatic rather than something you would translate word for word in normal English.

Also, lo here is neuter, not masculine. It does not refer to la integridad. It is part of the set expression lo que.

Because the expression is respectar a algo/alguien in this meaning of to concern / to relate to.

So you say:

• en lo que respecta a la integridad
• en lo que respecta al precio
• en lo que respecta a nosotros

That a belongs to the pattern of the expression.

The la is a direct object pronoun meaning it, and it refers back to la integridad.

• la integridad is the topic introduced first
• la comprobamos = we check/verify it

Spanish often does this when the topic is introduced separately at the beginning of the sentence. In English, we might say:

• As for integrity, we check it.

That it in English works the same way as la here.

Without la, comprobamos would be missing its direct object.

Yes. Comprobamos la integridad is a perfectly normal sentence meaning We check/verify the integrity.

The version with En lo que respecta a la integridad, la comprobamos does something extra: it highlights or sets up la integridad as the topic.

So the difference is roughly:

• Comprobamos la integridad = neutral statement
• En lo que respecta a la integridad, la comprobamos = As for integrity, we check it

The longer version sounds more formal and more contrastive, as if the speaker is going through different points one by one.

It can be either, because the nosotros form of some -ar verbs looks the same in the present and the preterite.

So comprobamos can mean:

• we check / verify
• we checked / verified

Only context tells you which one is meant.

In an isolated sentence like this, many learners would assume present unless the wider context suggests a completed past action.

Comprobar usually means:

• to check
• to verify
• to confirm

It is often used when you make sure something is correct, true, complete, or functioning properly.

Depending on context, la comprobamos could be translated as:

• we check it
• we verify it
• we confirm it

Because integridad is a feminine noun.

A useful pattern is that many nouns ending in -dad are feminine:

• la ciudad
• la verdad
• la calidad
• la integridad

So the article is la, and the pronoun that refers back to it is also la.

It sounds fairly formal, especially because of En lo que respecta a.

In everyday speech, Spanish speakers might prefer shorter alternatives such as:

• En cuanto a la integridad, la comprobamos.
• Respecto a la integridad, la comprobamos.
• La integridad la comprobamos.
• Comprobamos la integridad.

Your original sentence is correct, but it sounds like something from a report, presentation, meeting, or technical explanation rather than very casual conversation.

Because the first part, En lo que respecta a la integridad, is an introductory topic phrase.

The comma helps separate:

• the topic being introduced from
• the main statement

So the structure is:

• Regarding integrity, we verify it.

This kind of comma is very common in both Spanish and English with introductory expressions.