I've now fitted the bb, just thought I'd add a couple of details in case anyone looks this up in the future.
The answer to my actual question is that, as I removed the old bb I found grease from the original install, by the "cups". So I basically cleaned the shell as best I could, but just with a dry kitchen towel, then regreased the area.
The whole removal/installation process was done in less than half an hour. I needed two specialised tools (this threw me a little, originally I thought only one tool was required). One tool to remove the bb, a second tool to install the new one. Both Shimano and Park do the tools (in the end I ended up buying the park tool to remove the bb, and the Shimano tool to install the new one), but whichever make, you need two tools. The removal tool also needed a hammer (ouch!), the installation tool also required an 8mm allen key, but it really was straightforward to fit.
Two observations. The first was that the part that came off was not exactly what
went on. I suspect this is just a "passage of time" thing, as the new part fits perfectly and was confirmed by a Giant shop as the correct part. The second.....well I was surprised just how hard I had hammer to get the old bb out. (I started off with a mallet but that was no good at all.) I suppose this could have been something to do with me thinking, every time I hit the removal tool, "I hope I don't break anything". But in the end everything was fine.
The bottom bracket I fitted was a Shimano BB9141B. This is the better quality of two compatible bottom brackets (the other being the BB71). The differences between them seems to boild down to Ultegra versus Dura Ace.
The tool I used for removing the old bottom bracket was the Park BBT90.3. Seemed to be fine, buying the Shimano version of this tool would have cost a small fortune for some reason.
The tool I used to fit the new BB was the TL-BB12. Made the job a doddle but very expensive for something I used for half a minute!