Oh…I have some cards/ envelopes delivered with pen cancellation too. 
I guess the safest way is to go directly to post office and ask for hand cancellation, like @tpuchalski said. But it’s not as convenient as just inserting the cards to a postbox.
Thank you @Sigiriya for always sending cards with the protective paper on top of the image side. 
It was her card that I showed in pictures, a few post earlier.
It’s a great idea, and a really thoughtful one too.
When I go to my local USPS post office and ask for them to hand cancel, they’re willing to do it. One time I even showed up with 100 postcards for world postcard day and they were nice about it! However, the postcards I send still go through the machine to get sorted and cancelled again with the machine. So the recipient has a card with the nice hand stamp and the smudgy black machine stamp. And of course the machine might nibble the paper of the postcard too…
I get the scratched off message area damage every so often, which annoys me as much as when USPS scratches the front image.
You are one of the lucky people HAHA My PO says Hand stamping is a myth lol and never has any decent stamp sheets to offer aprart from the US flag ones 
Not all Post Offices here offer hand stamping or are even friendly and generous to talk about it.
Another bit of info from an ex-mail carrier - for those of you bemoaning the stamps being lined through with a pen or marker, unfortunately, that’s post office policy. If a mail carrier sees a piece of mail with an uncancelled stamp, they’re supposed to line thru the stamp so it can’t be used again. Most times they don’t bother.
Also, I want to apologize on behalf of the clerks people have mentioned who refuse to hand cancel postcards at the post office counter. That’s just bad customer service.
Thanks for the info @tpuchalski but I think I read in the official postal manual that it is not recommended to strike the stamps with a pen or marker and should be correctly canceled. Also I donot understand why many pen cancel a perfectly good already canceled stamp? Is there a reason behind doing this double cancelation? Pardon me If I am not aware of the rules but this somehow doesn’t feel okay.
Thank you for the info! Yes, I know about that practice, though it still doesn’t make it any better… 
But if you look closely, those, for example, in fact WERE cancelled correctly with a round stamp, so there were no reasons to spoil them with the marker and pen. Yes, it’s pale, but it’s there and in fact quite visible. And there were many other instances when my addressees complained on such marker cancellations despite the presence of normal hand-cancellation.
When I can, I go to the post office to hand cancel the cards and most of the times I meet very nice postal workers who never denies me the service. And I’m very thankful to them for it! 
Only once there was an unpleasant experience when a postal worker didn’t want to hand cancel the stamps for me: she said that if I want them hand-cancelled, it costs a different price, but after arguing she finally did it (with a very disgusted expression on her face) and in the end also blamed me for holding up the queue. Can you imagine?! I had literally one single postcard to cancel, which is a matter of seconds in fact, she was arguing with me about it for several minutes, but turns out it’s been me who was holding the queue! 
Now every time when I’m in line in my post office for any reason, I pray to all existing Gods that she’d be busy with some other client when it’s my turn, and I get some other clerk 
You could using something like a sanitizer, nail polish remover or anything with alcohol content to remove the stains. Try not to scrub too hard as it can peel off the image.
That is so insane and unprofessional of them to treat you like that way. Its not like we are asking for something so unreasonable in the first place and you have to pay a different price is the most ridiculous thing I have ever heard. Sorry to hear that you had to go through with that. Exactly my point whats up with scribbling all over when the stamps are already canceled 
its just pure vicious thing to do.
The horror! 
Suddenly it seems that the post office in Cleveland, Ohio is cancelling every postcard I mailed recently on the picture/wrong side. I just found this discussion from last year. I think with the constant increase in the cost of postage the USPS should be kind to Postcrossers!!
That’s what (covering postcards with a sheet of paper) I do with the postcards I send, and I ask people who send postcard to me to do so too if they can. I am so frustrated! I have lived in several countries, and nowhere have I seen postcards trashed so badly.
I have a question: has a petition or something similar been submitted to USPS regarding this issue? Have these issues been already brought to their attention? Complaining on the forum is not going to help anyway. I don’t want to accept what USPS is doing to my mail. I’m serious, I’ve never seen any other mail service disrespect the mail so much.
So, could we possibly do something about it?
I prefer the pen and hand cancelling marks over the usual heavy handed USPS 3 bar wavy line cancellation which obliterates and blacks-out everything it touches including the stamps, forum information, sender IDs and parts of the written message.
