İster indirimli ödemeyi ister itiraz dilekçesini seçsin, tebliğ tarihini kontrol etsin.

It means whether ... or ... or either ... or ....

So:

• İster indirimli ödemeyi ister itiraz dilekçesini seçsin
  = Whether they choose the discounted payment or the objection petition

This structure presents two alternatives and says that the rest of the sentence applies in either case.

Not really, at least not in the normal lexical sense.

Even though ister is also the 3rd person singular form of istemek (he/she wants), in the pattern ister ... ister ... it works as a fixed linking structure meaning:

• whether ... or ...
• either ... or ...

So here you should understand it as part of a set expression, not as wants.

They are in the 3rd person imperative/jussive form.

The ending is -sın / -sin / -sun / -sün, depending on vowel harmony:

• seçsin = let him/her choose, he/she should choose
• kontrol etsin = let him/her check, he/she should check

In English, this form is often translated in several ways depending on context:

• let him/her ...
• he/she should ...
• they should ...
• in official language: the person concerned should ...

In bureaucratic or legal Turkish, this form is very common.

Because one verb can apply to both alternatives.

The sentence is basically a shortened version of something like:

• İster indirimli ödemeyi seçsin, ister itiraz dilekçesini seçsin, tebliğ tarihini kontrol etsin.

But Turkish often avoids repeating the same verb if it is already clear. So:

• İster X ister Y seçsin
  is a natural compact way to say
• Whether they choose X or choose Y

Because they are direct objects.

Here:

• seçmek takes a direct object: choose something
• kontrol etmek takes a direct object: check something

So the nouns appear in the accusative:

• ödeme → ödemeyi
• dilekçesi → dilekçesini
• tarihi → tarihini

In this sentence, these are specific items, so the accusative is expected.

Because these nouns are built differently.

1. indirimli ödeme

This is basically adjective + noun:

• indirimli = discounted
• ödeme = payment

So the accusative is simple:

• ödeme
  • -yi → ödemeyi

2. itiraz dilekçesi and tebliğ tarihi

These are noun compounds in Turkish.

• itiraz dilekçesi
• tebliğ tarihi

In this type of compound, the second noun already carries a possessive-looking ending:

• dilekçe-si
• tarih-i

Then when the accusative is added, Turkish uses a buffer n:

• dilekçe-si-ni
• tarih-i-ni

That is why you get:

• itiraz dilekçesini
• tebliğ tarihini

They are indefinite noun compounds.

This is a very common Turkish structure where one noun modifies another noun:

• itiraz dilekçesi = objection petition
• tebliğ tarihi = notification/service date

Formally, the pattern is:

• first noun: bare form
• second noun: takes the compound suffix, usually -(s)I

Other examples:

• öğrenci kartı = student card
• otobüs durağı = bus stop
• kimlik numarası = ID number

So dilekçesi and tarihi are normal forms inside that compound pattern.

Because kontrol etmek is a common Turkish compound verb:

• kontrol = control/check
• etmek = to do/make

Together:

• kontrol etmek = to check

This is very common with many borrowed nouns in Turkish:

• yardım etmek = to help
• fark etmek = to notice
• iptal etmek = to cancel

So kontrol etsin simply means let him/her check or he/she should check.

The subject is understood, not stated.

Because seçsin and kontrol etsin are 3rd person singular, the implied subject is something like:

• he/she
• the person concerned
• the applicant
• the recipient

In official Turkish, this often works as a generic third person. English may translate it as they or as a role like the person should check.

Turkish often leaves pronouns out when the verb form already shows the person.

In this kind of sentence, it is usually best understood as a formal instruction or directive.

So it is not exactly as direct as speaking to someone with kontrol et, but it still has an official force:

• kontrol etsin = they should check / let them check

In notices, forms, and legal language, this is a normal way to give instructions about what a third party must or should do.

It is natural, but it sounds formal and bureaucratic, not casual.

Words like:

• itiraz dilekçesi
• tebliğ tarihi

already make the sentence sound official.

A more conversational or alternative phrasing might be:

• Hangisini seçerse seçsin, tebliğ tarihini kontrol etsin.

That still sounds fairly formal, but a bit smoother and more typical in many contexts.

If speaking directly to someone informally, Turkish would more likely use a 2nd person form instead.

Yes, that is possible, but it creates a slightly different structure.

For example:

• Hangisini seçerse seçsin, tebliğ tarihini kontrol etsin.

This means something like:

• Whichever one they choose, they should check the notification date.

Your original sentence uses ister ... ister ... seçsin, which explicitly names the two alternatives.
The seçerse seçsin type focuses more on whichever one is chosen.

Both are possible; the original feels especially suited to formal written language where the two options are listed clearly.