“We are pretty tired of talking about getting punched in the face,” says Chris, a 29-year-old American woman whose second name you don’t know but whose face – distressed and covered in blood – is likely to have become shockingly familiar in the past week.

Chris and Melania Geymonat, who is 28 and a doctor from Uruguay, were travelling home on a night bus, late on the evening of 30 May. They must have kissed, they think, or otherwise given away that they were on a date. To a group of young men, also sitting on the upper deck of the almost deserted N31 to Camden, that was taken as permission to shout abuse, ask how they had sex, demand, in Chris’s words, that they “perform”.

When one of them started throwing coins, Chris got up from her seat to remonstrate. In a few moments she had suffered a violent attack that left her with a broken jaw and battered nose. Geymonat, who quickly went to her aid, was punched so forcefully her nose was broken, and her bag and Chris’s phone were stolen.

Shocked, bleeding heavily and weeping, they asked a sympathetic fellow passenger – who was distressed to the point of tears by what had happened – to take a photograph. A few days later, having spoken to their families, they decided to post it on Geymonat’s Facebook page.

“When it happened, we were really angry,” says Geymonat, who is currently taking a year’s sabbatical from her medical studies to travel and work in Europe. “We decided to tell the story, because this situation needs to change, and maybe this helps a little. For me, it was a moral obligation. This needs to stop.”

We decided to tell the story, because this situation needs to change, and maybe this helps a little Melania Geymonat

They were entirely unprepared, however, for what would happen next. News organisations across Britain and the world picked up the photograph and the story. Geymonat’s Facebook post attracted tens of thousands of shares and comments. Theresa May described the attack as “sickening”, adding: “We must work together to eradicate unacceptable violence towards the LGBT community.”

Jeremy Corbyn, the Labour leader, the mayor of London, Sadiq Khan, and the equalities minister, Penny Mordaunt, all tweeted outrage. In Uruguay, where the population is less than 3.5 million, “everybody knows my name now and my sexual orientation”, says Geymonat. “Which is private – or was.”

Two weeks after the attack, and a week after the pair became a global focus for sympathy, outrage and trolling, the two women are physically recovering. Geymonat had surgery on Wednesday to correct damage to her nose; Chris has been told her jaw will heal by itself within a few months. Five young men aged between 15 and 18 have been arrested and bailed until a date in early July.

The women are still angry, however, and quietly determined to see something positive comes from the violence they suffered.

Their experience of the past fortnight has left Chris in two minds. She chose early on not to reveal her second name in a bid to maintain some privacy (her mother, she says, was amused to read a blogpost asking “Is this Chris too poor for a surname?”).

She says: “On the one hand, it has got people talking for the right reasons. I think it has made people feel more comfortable sharing their own stories of hate crime and routine discrimination that I think people don’t necessarily feel goes on.”

On the other hand, it has been frustrating watching the media coverage spiral beyond their imaginings and out of their control, “because it was very telling of who society values and is willing to get upset about”.

What does she mean? “Well it is, regardless of who is in it, a very striking picture. Two bloody faces … And it certainly doesn’t hurt that we are both white, we are both conventionally attractive. I think it begs the question: why do we need this sensational, clickbait-y, graphic [image] to engage people in a story like this? Because we got hit in the face. Other people get murdered or mutilated, or disabled for the rest of their lives.”

She does not believe others who do not look like them would have attracted the same coverage? “If you can show me the example where someone has gotten similar, then all right. But I can’t think of an example.” Geymonat mentions the story a friend told her of a Brazilian man who was punched so violently he was left in a wheelchair, “and that story didn’t go worldwide”. They have nothing but praise for the police response – “We got the red carpet rolled out for us,” says Chris, “but I just wonder how other victims of hate crimes, how their experience would compare.”

The violence aside, it was not a particularly novel encounter, she says. “I have been out with women [on dates] before, and every single time, I am going to assume they were heterosexual men, interrupted us. We were just doing our thing, existing. And I think there is this entitlement men feel, to women, and especially two women together. They feel like our sexuality is for their entertainment.”

Both argue powerfully for the violence they experienced to be seen not only as homophobic but also misogynistic hatred; Geymonat says many of her heterosexual friends have suffered similar violence “in which they were condemned … as being the provocateurs. Just because maybe they were nice, they were wearing a skirt, maybe they had drunk two beers.”

They did not ask for this platform, says Chris, but now that they have it, they feel compelled to speak out. In an opinion piece published in the Guardian on Friday, she urges those who were shocked by their story to remember other hate crime victims (“make the extraordinary reaction to our attack the norm”), hold politicians and corporations to account, and “stand up for yourselves and each other, and fight back”.

She is determined not to be afraid to show affection in public in future, she says. “To not hold someone’s hand and be affectionate in the way heterosexuals do, to me that is kind of cowardly. People fought really hard for much more and gave up a lot of their own safety to fight for it. And so to say I’m scared? Come on.”

“I am having a hard time these days to climb upstairs on the bus,” says Geymonat, but she, too, says the attack will only make her more determined. “It will change my behaviour, definitely, towards the activism I feel we need to do. It’s a commitment I now have to follow.”