Connecting Amazon Echo Dot to smart TV

I'm wondering if anyone here might be able to help me with this.

We've bought a Amazon Echo Dot for my Grandma who's no longer able to see very well. The idea was to connect it to her Smart TV so that she would be able to navigate it using voice commands rather than the remote (which she can't see).

I've been able to add the TV as a device on the Alexa app, however I'm unable to get Alexa to carry out any commands on the TV - change the channel, open an app etc.

I believe that what I need to do is connect the TV to the Echo Dot via Bluetooth. Is this correct? Is it functionally a different thing than having something as a device in the app? Currently when I go to the TV under devices and click to manage linked Alexa devices, the Echo Dot is greyed out because it's already paired with a device (presumably the iPad where I've downloaded the app as there are no other devices connected).

If the lack of bluetooth connection is the issue, I'll need to buy a Bluetooth transmitter for the TV has it doesn't have bluetooth capability. So I just wanted to see if anyone had any advice for me before I invest in another piece of tech.