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 İade is an Arabic word and it means return or give back. When you say "geri iade" you say something like give back back. This seems absurd but foreign words gain different meanings in other languages. When you say "geri iade" in Turkish it makes sense. I guess Turks give a meaning to iade as  "to give " and they use it with "geri (back)". This is a very normal thing. This is called semantic shift.

 I don´t teach Turkish. And I always said I hate grammer. Check my profile. I am not interested in Turkish grammer. I am only interested in literature and philosophy. I can easily accept that I am wrong when I made a mistake. I  said people don´t obey the rule. I haven´t denied such a grammer rule. If people don´t obey the rule, it has to change. It is what I want to say.

 It is not important if I say so. It is important if people say so. You can´t do anything. I think people say "nüans farkı" and maybe they will say the others. You have to accept it. Do you have any objection to wrong usage of serbest, peş and many others?

"geri iade" can seem you idiotic but it is not. There can be such  semantic shifts in languages. For example serbest means "başı bağlı(dependent)" in Farsi but it is the opposite in Turkish. Also peş means "ön(front)" in Farsi but we use it as "arka(back)". Even if you think  it is idiotic to use them this way you can´t do anything to stop people. Because only people can decide what is proper to use in any language not linguists. If you try to set rules people don´t obey you will create another language; an elite language like Ottoman Turkish. You should accept the language as it is. Language is like a living organism. It grows and changes. Nobody can stop this. Grammer rules also have to change. They are not like ten commandments.

 Thank god a good explanation. But i googled this and the results are interesting.

"Adamlar geldiler" 2.600 results

"Adamlar geldi"  15.500 results

As you can see people prefer not to obey the rule. Why? Because people always prefer the shortest way to say something. Because of that many words, verbs changed. They became shorter. Also rules can change.

"both my children" means "her iki çocuğum"

"male both" means "(her) ikisi de erkek"

By the way there is not such a rule as you can´t use two "ler" in the same santence. Sometimes I prefer to say so sometimes not.

Onlar geldiler. (When you google it you find 6.790 results)

Onlar geldi. (When you google it you find 21.200 results)

Most of the time I prefer the second one.

 Sentence has two parts. In the second part there is a hidden subject "onlar" When we don´t say it we should use "ler" at the end of the verb to point out the plurality.