The thing is that I can not say anything without having access details as it can be anything. With the page you shared hidden link , I can see "Page Not Found" error.
To help you further I will require access details so I can see the problem or you can send me duplicator copy of your site.
Ah you're right it was set to private, you could not view it - sorry.
Changed it now so you can view it.
Unfortuntely I'm not allowed to provide you with a duplicate of the website.
I've now managed to show the grey twitter icon, please view: hidden link
I had to replace "return" by "echo".
It also has the correct link url href="hidden link" in the code - but the icon is not linked? Please advise.