I get the extra LTR characters if I try to follow that link. Don't you?

No. The link provided by PerlMonks is to https://metacpan.org/pod/Business%3A%3AStripe%3A%3ASubscription.

Screenshot of HTML (And no, it contains no hidden/special characters.)

If you get something else, your browser (incl extensions) or your proxy is changing something.

The source in my home node has this...

<p>CPAN Releases</p>
<p><a href="https://metacpan.org/pod/Business::Stripe::WebCheckout">Bu
+siness::Stripe::WebCheckout</a><br />
<a href="https://metacpan.org/pod/Business::Stripe::Subs&#x200E;crip&#
+x200E;tion">Business::Stripe::Subs&#x200E;crip&#x200E;tion</a><br />
<a href="https://metacpan.org/pod/Business::Stripe::Webhook">Business:
+:Stripe::Webhook</a></p>
<p><a href="https://metacpan.org/pod/AI::Embedding">AI::Embedding</a><
+/p>
[download]

It is the &x200E; characters that should not be there...

They were not put there when I edited my profile but somehow PM is adding them and I cannot get rid of them...do they not look like that to you?

I've turned off all browser extensions and checked on another machine with a freshly installed Chrome browser with no extensions.