grief tourist
n. A person who travels to the scene of a recent tragedy to mourn the victim or victims.
Examples
2004
The commentator, Francis Wheen, has labelled the frenzied pilgrims that trekked to Soham the "grief tourists". Grieving over two girls they didn't know and a tragedy they couldn't possibly understand. Trampling on a tiny village's space and memories, full of Tennyson's idle tears, to gratify some need in themselves.
—Gwen Halley, “Grief tourists lap up other people's pain,” The Sunday Independent (Ireland), March 14, 2004
2003
He courted the attention of the Press, proffered unsolicited information, sought to listen in on police conversations and behaved with the same bottomless vacuity as the busloads of gawpers who descended upon Soham last year, the so-called 'grief tourists', whose attitude transforms murder into a shameful entertainment.
—Brian Masters, “A study in evil,” Daily Mail (London, England), December 20, 2003
2002 (earliest)
Of course what happened to those two children was horrific beyond belief. But we are kidding ourselves if we think that what we feel is anything at all compared with what the families of Jessica and Holly are going through.

The senseless slaughter of these two children was a very private tragedy. The rest of us can sympathise, it would be strange if we did not, but we should go a little easy on the public weeping and wailing.

It is good that we have become more demonstrative of our emotions over the past 10 years.

But let's not become a nation of grief tourists.
—Tony Parsons, “Comment on footballers observing minute's silence,” The Mirror, August 26, 2002
Notes
Traveling to the scene of a tragedy is also called dark tourism (1997) and the people who do it are said to be jumping on the grief bandwagon (1998). They're indulging in grief-lite (1997), recreational grief (1998), or mourning sickness (1998). All of these terms were coined in the months after Princess Diana's death in August, 1997, and they provide lexical evidence of a cynical backlash against the massive outpouring of grief that followed her death.

Thanks to Brian Sidlo for passing along grief tourist and some of the related phrases.