Can I send third party checks to pay my tax return?

That is a really bad idea.  No.  Why would you even want to do that?

I was asking, the bank account I have doesn’t give checks, so my grandma wanted me to send her the money so I can pay it

Instead of engaging in all that confusion with Grandma--how about go to a drugstore and get one of those pre-paid Visas or master card and pay it with that if you do not have a credit card?
 Or if you have a debit card, go online with the IRS and pay directly?<a rel="nofollow" target="_blank" href="https://www.irs.gov/payments/direct-pay">https://www.irs.gov/payments/direct-pay</a>

You don’t have to be rude about it.

Or you could purchase a money order and mail it.

You (or she) can pay directly here:

https://www.irs.gov/payments