Well you could determine that they have created an alternate timeline/parallel universe and get violently expelled back into your game universe. Aletrnatively have this cause a time storm that requires the sacrifice of your timelord's current incarnation to rectify.
If your story is set before the fall of the Time Lords then the Time Lords will trap that alternate pocket of space-time inside the Axis the PCs will have to escape that.
Whenever another species causes enough temporal distortion to damge the Web an Interventionist (probably the CIA) is sent to prevent the species from causing further damage. If that Time Lord doesn't return then the Time Lords (again, probably the CIA) has that Time Lords personal timeline shut down effectively removing that worlds timeline from history (apparently to be replaced by one where the temporal damage never happend in the first place). This prevents the missing Time Lord from being used to damage the rest of the Web. The alternate timelines are attached, in a spoke like pattern, to the Axis, which is located in interdimensional space. The Overseer, from the sideways dimension of Guardus, supervises the Axis. Each of these timeline is trapped in a giant loop. While most of the timelines in the Axis are created by the Time Lords some are produced by other species.
Perhaps the paradox has created a viable, stable parallel universe, similar to Pete's World, rather than a time spur that will be destroyed by the Reapers. The players now find that they are in a different universe - there may even be alternative versions of themselves. If they want to get back to their true home, they'll have to work out the means to do this without ripping a hole in reality - which may be an adventure in itself.
My take is that its a 50/50 chance which timeline the Reapers will go after [which is why most of my PCs don't mess around with changing history - 50/50 chance of being eaten!]
But if the original Universe was the one that go eaten then I guess this is all they've got. If they grow to hate it then they can try to change it so that is more closely resembles their original timeline - but that means another 50/50 roll of the dice with the Reapers! ;D
I'd definitely go with a 'Father's Day' scenario the first time around, with Reapers and such.
If I've already used the Reapers, I'd shunt the players off into some sort of hell-dimension of an alternate universe, where things are much darker and dangerous and it will take them an entire series of adventures and a great deal of risk to find their way home.
If they screw up a third time, I'd have the Time Lords put them on trial for their lives, or, in the post-Time War universe, make the changes irrevocable and possibly have them blotted out by some strange quirk introduced as the universe takes its new form (perhaps a universe where the Time Lords never existed and the Doctor is only a fictional character on television... oh, wait, has that already happened...?)...