How can I tell if my 32.5, 110, and HiCap have been recapped?

Calling re-cappers seems like a potentially laborious process of elimination.

I think Brad is looking for a more definitive lids-off means, if it exists.

Try contacting your most likely local 're-capping facility'. Or ask who you bought them from, where they were done.

Do Naim keep track of the work done in ''authorised'' service centers outside their own factory including the ones in North America?

Most definitely - the practice in the United States was to note the month / year of recap on the bottom of the large reservoir capacitors (as well as the technician's initials), on devices such as Hicaps & NAP 250/135s. Chris @ AV Options should have all of the historical service information for the United States (including ASL Group & NAIM Inc service history as well, if I recall correctly).

Thanks all.  This is helpful.  

To take the surround extrusion off, do I take the feet off?  I'd like to have a look see.  

Since I've had the units for a while now, they are going to need a service soon anyway.  I don't want to spend a ton - it looks like the pricing from Class A is reasonable?  Any recommendations on recapping?

If you unscrew the feet, you just slide the innards backwards. If you do it forwards, you might scratch the bit you see at the front. 

If if you are in the uk (stating your location in your profile is helpful) Darran at Class A will discuss what is best with you. 

In the case of my hicaps, there is a four digit number on the large black reservoir caps That are the last two digits of year, and two digits for the week of manufacture.  The cap's in both of my hicaps are labeled "0650" which means December 2006 (week 50).

Spot on, with both points there, @HH. 

Would have been much easier if the OP had stated his location.....

Darran @ClassA is highly recommended.....!

I'm in Seattle, WA, USA.  

AV Options looks and sounds great, but there's no way I'm going to pay a $1000 x 3 for recaps.