you don’t need to do anything about the certificate. Just accept it in your local network.
I think you are confused with secure/unsecure realted to local/remote a bit. In your local network, you (basically) don’t need to bother about unsecure(http) oder secure (https) connection. As long as you know what happens in your network and which devices/persons are in it, it’s fine.
There are several ways for remote connection and all are documented and throughly discussed in this forum. The easiest way ist to us myopenhab, which is funded by openhab e.V. If you create an account there and connect your OH instance with it, the connection is secured by https.
You can forget this as @NoneWhereTo stated. Not needed for a remote connection. It is a way to make the connection even more secure and passwordless. Google tells you about certificates if you wan’t to know more.
I would also recomend you to use myOpenHAB for easy and secure remote connection.
In fact that one is opened when touching the question mark in the screenshot
Maybe we could/should improve context by linking the help icon to a short docs page giving a bit of context, which then links to the discussion thread.