UPDATE: 25/07 

Be sure to have the rent receipts and other relevant document proof with you if you are claiming HRA/Section 80 deductions in the tax return directly. They are not needed at the time of filing, but after your tax return is submitted and processed, the Department may ask you to upload supporting documents on the Income Tax website. 

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There are still ways to save tax and you can even get a refund from the Income Tax Department in case your employer has deducted higher taxes.

Read this article to claim exemptions and deductions, even if you've missed the investment proofs submission deadline: https://cleartax.in/guide/what-to-do-when-you-miss-the-income-tax-proof-submission-deadline