The phrase "arguably damage" is correct and usable in written English.
It can be used when discussing a situation or action that may cause harm or negative effects, but where the extent of that damage is open to interpretation or debate.
Example: "The new policy could arguably damage the company's reputation among its loyal customers."
Alternatives: "potentially harm" or "possibly injure".
Similarly, when Rolling Stone published an account of an alleged gang rape at the University of Virginia without seeking out the accused, and likely got the story wrong, it arguably damaged the credibility of sexual-assault victims on that campus and elsewhere.
It's kept its end up at the box office over the past five years, but a chain of sequels – Toy Story 3, Monsters University and Cars 2 – had worrying echoes of parent company Disney's cash cow-flogging tendencies, and has arguably damaged its integrity.
Ramsay's "hilarious" outburst over a vat of minced beef might do numbers on Twitter, but his style of abusive management has arguably damaged an entire generation of chefs.
(Statement in February 2007) Now Arguably the damage was done to Murdoch Senior during his testimony to MPs last month, which made clear that he had, at best, taken his eye off the ball when it came to the running of the NOTW.
By February 6, the online article had been deleted, but arguably, the damage was already done.
Arguably more damage than the phrase "bring home the bacon" which nobody has ever actually said out loud ever.
"[There] was good reason to worry that the UK, as the country arguably most damaged by the banking crisis and with the largest fiscal deficit in the G20, could lose the confidence of creditors without a credible plan for deficit reduction, including an early demonstration of commitment... Almost three years later, the question is whether the balance of risks has changed".
However, arguably the greatest damage done by Obama is his continuation of the "war on terror" policy, which has destabilised Africa, led to an upsurge in religious fundamentalism and undermined economic growth.
These sorts of manoeuvres are sure to cause a huge row, and thereby arguably do more damage to the world's poor than climate change will.But America will never consent to a more stringent set of environmental standards through the WTO.
Vicious fighting destroyed the country, and the Islamic Republic's stature arguably suffered more damage than if he had fallen swiftly.Support for the slaughter of Syrian rebels destroyed much of the goodwill Iran had painstakingly garnered among ordinary Arabs over decades.
