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Apparently it's a common way to write this phrase, at least on the web.
見てみてください
What's up with that?
I first encountered it on weblio
Some examples, the first results from google
https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1443775544
https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q11197208331
Those two「みる」have different meanings and functions here.「みる」corresponds to several different verbs with different meanings and functions. To list a few: 「みる」、「見る」、「診る」、「観る」、「視る」、「看る」. Using different kanji suggests different shades of meaning and emphasis. 「見る」is the most commonly used rendition simply meaning "to see/look" in a generic sense.
「てみる」means to give something a try, to try and do something and see how it goes. It is usually written in kana, pursuant to official guidelines. The orthography of kanji and kana use has been codified in a cabinet directive 公用文における漢字使用等について（昭和56年内閣閣第138号）which specifies suggested usage and orthography.
次のような語句を，( )の中に示した例のように用いるときは，原則として，仮名で書く。
例
略...
・・・てみる(見てみる。)
The boldface words read:
...(these phrases) should be written in kana, in principle
And the example I quote here is exactly what you are asking about.
Therefore,「見てみる」means "to try and take a look" and usually translates as "take a look" with the suggestive "try" part implied. So 「見てみてください」would be "Please take a look."
