TSA check persons and luggage departing from ana US airport for security purposes.
So no, they won't be involved anywhere on a Mumbai-New York flight.
It will be the local Indian equivalent who will check your luggage (and you). If by phone stands you mean some passive device (probably made mostly of plastic and/or metal) which is just used to hold up the phone, then I don't see any reason they would have any issue with them.
If your phone stand is more than that, then it depends on exactly what. For instance if it includes a battery (i.e. acts as a power bank), then there may be issues depending on the number. Other types of "active" phone stands (e.g. with induction charging) should not be an issue for security purposes.
When you arrive in the US, you will however go through Customs (part of CBP), after you have gone through passport control and reclaimed your luggage.
Before you get there, you will have to fill in a Customs Declaration, form 6059B. I believe you can fill the form on the kiosks or via an app nowadays.
- You will have to tick the "Yes" answer to the "I have (We have) commercial merchandise" question. The form defines commercial merchandise as "(articles for sale, samples used for soliciting orders, or goods that are not considered personal effects)".
- You will have to enter the value of the items next to "VISITORS—the total value of all articles that will remain in the U.S., including commercial merchandise is". As explained overleaf, "For gifts, please indicate the retail value".
- You will have to enter the description and value at the bottom of the second page.
As explained on the second page of the form:
CBP officers will determine duty. (...) Visitors (non-residents) are normally entitled to an exemption of $100. Duty will be assessed at the current rate on the first $1,000 above the exemption.
Note that since those are commercial goods it's quite possible you don't qualify for the $100 exemption at all, but I haven't checked.
Duty rates usually vary anywhere between 0 and 6%, but there's a lot of variation. You can check rates in the HTSUS.