Not pseudo-1998... but very "several years old" looking in general
Reading that comment about the site looking like it was designed in 1998, I assumed it would be an unsuccessful attempt at the current "flat" design aesthetic (*), i.e. not literally 1998 but overly plain. That'd at least suggest they knew what they were going for but not quite getting there. In fact... no.
The small "TSB" logo actually has *jaggies* round the circles, like it's been rescaled without antialiasing. That, at least, *is* something I wouldn't expect to have seen for the main graphic on a corporate site in this millennium. As for the rest...
The tabs use that now-dated shading, gradients and rounded edges, and the whole thing looks small and shoved to the side even on my 1280 x 1024 4:3 monitor. It actually *does* have a very dated feel to it... maybe not 2003, but certainly 2003-06.
(Okay, maybe the use of pink and sky blue is a nod to a more recent colour trend, but even that seems to have passed its peak a while back).
(*) Something I do find refreshing after the overuse of "plastic" effects and horrible bland gradient shading in the Web 2.0 era, and which can look clean and bold... but also carries the risk of looking flat and underdesigned if not done well.