Removing a password from a PDF you own
A PDF can carry two different passwords, and only one of them is a lock. Which one your file has decides what can be done about it.
Which password does my file have?
If the file asks for a password before it will open, that is the user password and the document is genuinely encrypted. If it opens straight away but printing or copying is grayed out, that is the owner password, and the content was never encrypted at all: the restriction is a flag that a reader chooses to honour.
The two are set independently. A document can carry both, either, or the same string for both, which is why one file refuses to open and another opens but will not print.
Can a password be removed?
The owner restrictions can be dropped without knowing anything, because they are a request rather than a lock. The user password cannot: without it the bytes of every page are encrypted, and no tool can recover the content of a file it cannot decrypt.
So removing a password means one of two things. Either you supply the password you already have and the file is written out without encryption, or the file only ever carried restrictions and rewriting it leaves them behind.
Is that allowed?
It depends entirely on whether the document is yours to open, and this suite cannot tell. Taking the password off your own bank statement so you can file it is ordinary housekeeping; doing the same to a document that is not yours is not, and no amount of technical convenience changes that.
Nothing here breaks encryption. There is no password guessing, no dictionary and no recovery mode, so a file whose password you do not have stays closed.
What should I do instead of removing it?
Often, change it rather than drop it. When the real problem is that the password is shared or forgotten by everyone who needs the file, setting a new one you control keeps the protection and fixes the access.
If the document is going somewhere that cannot handle encryption, such as an archive or a print shop, take the password off and then think about what else the file carries. Encryption hides the content from strangers; it does nothing about the author name and the editing history sitting in the metadata.
Where to go from here
Unlock PDF takes the password you have and writes the file out without it, and protect PDF sets a new one along with the permissions it should carry.
Redaction that actually removes text covers the case where hiding is not enough, and PDF privacy on the web explains why this happens in your browser rather than on a server.