The only worry I would have is if it got hot enough to ruin the plated-through hole. That second photo is telling; you can clearly see enough heat happened to reflow the solder on the end away from the slot.
Do you have a temperature-controlled desolder station? I wouldn't try this with solder wick or a cheap solder sucker, as those multilayer plated-through holes are fragile, and you don't know which layer the end of that cap towards the PCI slot is connected to. Gut feel is it connects to the internal ground plane, which would be good, but that's just a gut feel. The fact that the solder on the end towards the slot didn't reflow is good, and it would confirm a relatively large thermal mass, like a ground plane, is on that side. That will make desoldering a bit more difficult, though, as that ground plane will sink desolder heat just as well as it did the fault current heat.
Tantalums have a nasty habit of failing short-circuited, and significant damage to traces and/or regulators and other parts can occur when they fail.
If you decide to replace this one I would recommend shotgun replacement of all of that type on the whole board, as it is just a matter of time before another one goes pyro on you.