The stamp shown in the question is franked.
Here are a few real-word example sentences that unambiguously show franked in use in the required sense:
Robert Murray, www.stampshop.com
This article is presented here because of my unease about the present situation regarding the re-use and sale of UK stamps which have been through the post but escaped being postmarked ("cancelled"/"franked").
Daily Mail, 28 May 2009
The Royal Mail has launched a new tamper-proof stamp in a bid to stop people peeling off old ones and re-using them.
The fraudulent act costs the company tens of thousands of pounds a
year. The problem has thought to have recently increased as credit
crunch-hit customers try to get away without paying.
are franked when they go through the sorting office, the markings on
re-used ones are not always picked up by staff and so many slip
through the net.
Daily Record, by Jane Barrie, 25 March 2018
...we found fake and used first and second class stamps for sale for less than half their face value.
The counterfeits, which experts believe mainly come from Turkey and China, are missing the crucial phosphor bands printed on real stamps. Some also don’t carry date and source codes within the background lettering.
The used stamps are unfranked and advertised as for collectors only – but head illegally back into circulation.
The relevant definition from Oxford Living Dictionaries follows:
frank verb [with object]
1 Stamp an official mark on (a letter or parcel), especially to
indicate that postage has been paid or does not need to be paid.
‘Three were international mail franked by Bang Lamung Post Office on the 26th and 27th of last month.’
‘We had aggressively used computerized mailing lists in the Senate for
our franked mail program and in our political operations for direct
‘Volunteers stuck labels, folded letters, franked envelopes and filed
mail bags to send more than 10,000 copies of the new brochure out to
‘That form has since been well franked as Wild Passion is now one of
the leading lights of the Noel Meade yard.’
‘Royal Mail introduces new requirements for franked mail to bear a
return address for it to be returned when undeliverable’
‘Bargain hunters browsed around the vast array of stalls selling
anything from sunglasses to framed and franked Adolf Hitler stamps!’
These example sentences are a little confusing when read together as there are several related but distinct meanings to frank here. The two example sentences I have italicised refer to franking in the sense most relevant to the question.
Franking does not just refer to the cancellation mark. As the definition above indicates, a frank could, for instance, be an imprint used in place of a stamp, such as those seen on direct mail or on automatically generated post, such as utility bills or bank statements.
Hence, a franking machine refers to a machine businesses which send a lot of post use in place of stamps. Mailmark is the (UK) Royal Mail franking scheme:
The latest, most sophisticated franking machines can process huge
volumes of mail quickly and accurately – and even more basic models
offer major time savings. It’s easy to drop your Mailmark franked mail
at a Post Office®, or if you regularly send high volumes of Mailmark
franked mail, you can set up a regular business collection.1
So franked mail nearly always means post bearing a frank for postage rather than a stamp, something like this:
But it doesn't end there. The Wikipedia rendering of the Universal Postal Union technical meaning of franking follows, though this does not fully accord with day-to-day usage, as, according to this definition, an uncancelled stamp is itself a frank:
Franking refers to any devices, markings, or combinations thereof ("franks") applied to mails of any class which qualifies them to be
postally serviced. Types of franks include uncanceled and
precanceled postage stamps (both adhesive and printed on postal
stationery), impressions applied via postage meter (via so-called
"postage evidencing systems"), official use "Penalty" franks, Business
Reply Mail (BRM), and other permit Imprints (Indicia), manuscript and
facsimile "franking privilege" signatures, "soldier's mail" markings,
and any other forms authorized by the 191 postal administrations that
are members of the Universal Postal Union.
Frank does seem to be a rather confusing word, but, putting the Universal Postal Union definition aside, which is odd and legalistic, in normal usage frank's ambiguities don't generally cause any trouble.
As the term has such complexities to it - much more than I realised in the first instance - while writing this answer I found myself beginning to doubt that franked is the right word to use when referring to stamps. However an eBay search for franked reassuringly turns up lots like this:
Whereas unfranked will find you this sort of thing:
(Having said that, I can understand how you might well prefer this answer which gives cancellation and postmark, both of which also entirely correct and completely unambiguous. If you need a verb, it would also be quite proper to say a stamp has been cancelled or postmarked.)