I would greatly appreciate it if you could proofread my resume before submitting it.
I would greatly appreciate it if you could go over my resume before I hand it in.
Hello there.
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チェック、と言うのは間違えなどないかチェックするの意で間違いないでしょうか。
その場合は、"check it"ではなく、"proofread"や"go over it"や"check or mistakes"などはっきりと伝えた方がわかりやすいかもしれません。
"I would greatly appreciate it if you could proofread my resume before submitting it"
もしくは
"I would greatly appreciate it if you could go over my resume before I hand it in"
「提出」は"submit"ですが"hand it in"とも言います。
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Hope this helps!
日本 
