jqGrid uses jQuery UI CSS. jQuery UI don't support quirks mode too. The usage of quirks mode means that you are in the time before publishing of HTML 4 in december 1997. All web browsers created in the current year thousend (starting with 2000) support HTML 4. So I think that you should probably fix your code by including some statement.
If you don't use you can't use practically any recent JavaScript library. Even if some features will be work you will be definitively in not tested and not supported environment.
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