"Extraordinary claims require extraordinary evidence" is a staple. Welcome!

Thank you so much, I've been a member for a while now. But there was another frequently cited statement that can be used to refute these claims.

You might need to be a tad more specific. Which claims?

There's Hitchens's razor:
https://en.wikipedia.org/wiki/Hitchens's_razor
"What can be asserted without evidence can also be dismissed without evidence."

But there's no one quote that encompasses everything.

I was going to quote exactly this, but I don't think it fits what we do on this site. We dismiss with evidence.

We do both. Preferably with evidence, but a lot of the time we point out an absence of evidence (when that evidence would be expected) as evidence of absence. Also, (to Hitchens' point) an absence of evidence means there's no reason to believe in something, so you can equally disbelieve it (although then we have the issue of the equal weight fallacy)

Do you remember anything about the context where you saw it used, @Sebastian ?

Occam's Razor, or the principle of parsimony, is often quoted as
"Entities must not be multiplied beyond necessity" in English; originally Latin Entia non sunt multiplicanda praeter necessitatem
(Wikipedia, https://en.wikipedia.org/wiki/Occam's_razor).

More commonly it is paraphrased as
"The simplest explanation is the best".

External Quote:

(Wikipedia).

There are more complex variants along the lines of
"The simplest explanation that takes into account all the available evidence is usually the best".

What constitutes evidence, or relevant evidence, might be arguable.
The meaning of "simplest explanation" is sometimes misunderstood, for example if we're talking about the construction of the Giza pyramids, "Aliens did it" is a linguistically simple explanation which is easily understood, but it involves the "multiplication of entities" for which there is no evidence, i.e. intelligent extraterrestrial visitors in ancient Egypt, and it ignores available evidence about the evolution of pyramid building, known Egyptian abilities in quarrying and stonemasonry, etc. etc.)

Claims that can be asserted without evidence can be dismissed without evidence?