Η τράπεζα είπε ότι η χρέωση μπορεί να είναι λάθος και θα την ελέγξει αύριο.

Because Greek uses the definite article much more regularly than English.

• η τράπεζα = the bank
• η χρέωση = the charge

Both nouns are:

• feminine
• singular
• nominative (because they are the subjects of their clauses)

In Greek, common nouns usually take an article when they are definite. So τράπεζα είπε would sound less natural here than η τράπεζα είπε.

είπε is the aorist form of λέω (to say). Here it means said.

Why aorist?

• The aorist is commonly used for a single completed action in the past.
• So Η τράπεζα είπε means The bank said as one completed event.

Compare:

• είπε = said / stated
• έλεγε = was saying / used to say

ότι means that and introduces a content clause: what the bank said.

So:

• Η τράπεζα είπε ότι...
• The bank said that...

In English, that is often optional:

• The bank said the charge may be wrong

In Greek, ότι is very normal and explicit in this structure.

Because after μπορεί in this meaning, Greek normally uses να before the next verb.

• μπορεί = it may / it is possible
• να είναι = be

So:

• μπορεί να είναι λάθος = may be wrong

You should think of να here as a required grammar particle, not as a separate word you translate literally every time.

This pattern is very common in Greek:

• μπορεί να έρθει = he/she may come
• μπορεί να ξέρει = he/she may know

Yes, in function it belongs to the να clause, which is often called the subjunctive environment. But with είμαι, the form είναι looks the same as the ordinary present form.

So in practice:

• να είναι = to be / be in a να construction
• μπορεί να είναι = may be

For many verbs, the form after να may look different from other forms, but with είμαι this one happens to look familiar.

λάθος literally means mistake / error, but in everyday Greek it is also very commonly used in expressions meaning wrong.

So:

• είναι λάθος = is wrong / is a mistake

In this sentence, η χρέωση μπορεί να είναι λάθος means the charge may be incorrect.

This is very natural Greek. You will often see:

• Αυτό είναι λάθος = This is wrong
• Έκανες λάθος = You made a mistake / You were wrong

Because Greek often leaves out a subject when it is already clear from context.

In this sentence, the subject of θα την ελέγξει is still the bank. Greek does not need to repeat it.

So Greek says:

• Η τράπεζα είπε ότι ... και θα την ελέγξει αύριο.

English often also avoids repetition:

• The bank said that the charge may be wrong and will check it tomorrow.

If you wanted, you could repeat the noun for emphasis or clarity, but it is not necessary here.

This is the Greek future construction:

• θα = future marker
• ελέγξει = the form used here after θα
• την = it (referring to the charge)

So:

• θα την ελέγξει = it will check it / will check it

The verb comes from ελέγχω (to check / examine).

A useful contrast:

• έλεγξε = checked (past)
• θα ελέγξει = will check (future)

Even though ελέγξει may look unusual at first, after θα it is simply the normal way to form this kind of future.

την refers to τη χρέωση (the charge).

It is:

• feminine
• singular
• accusative
• a direct object pronoun

So here την means it.

Why feminine? Because χρέωση is a feminine noun:

• η χρέωση
• later replaced by την

Why before the verb? Because Greek object pronouns usually come before the verb:

• θα την ελέγξει = will check it

That word order is normal in Greek.

Because Greek first uses the full noun, then replaces it with a pronoun to avoid repetition.

First:

• η χρέωση = the charge
  This is the subject of μπορεί να είναι λάθος.

Later:

• την = it
  This is the object of θα ελέγξει.

If Greek repeated the noun instead of using the pronoun, it would be:

• Η τράπεζα είπε ότι η χρέωση μπορεί να είναι λάθος και θα ελέγξει τη χρέωση αύριο.

That is grammatical, but using την sounds more natural because the reference is already clear.

Yes. Greek word order is more flexible than English, though some orders sound more neutral than others.

The sentence as given:

• ... θα την ελέγξει αύριο

This is a natural, neutral way to say ... will check it tomorrow.

But Greek could also say:

• ... και αύριο θα την ελέγξει
• ... και θα την ελέγξει η τράπεζα αύριο
  (less neutral, more emphasis)
• Αύριο θα την ελέγξει
  (puts more focus on tomorrow)

So the meaning stays basically the same, but the emphasis can shift depending on word order.