The only way I know of to record a track onto the SD card on that model, is to have it log automatically. (edit - this is not the default setup.) These logs are .gpx files and do include the timestamp (UTC) as in GB's example above.
The filenames indicate the date each logfile was written.
You can just remove the card and put it in a card reader and copy the files to your PC, then do whatever with them. Or you can connect the GPS and push it into 'data storage mode' to see the card as an external drive. Just connecting in the normal way, you won't see the card. If you don't know how to do 'data storage mode' then its easier just to use a separate card reader.
Your 'Active Log' may also contain the information you want (if it was a recent event and you haven't done much since) and that is very easy to download just through the normal connection methods, because it exists in the GPS 'user memory', not on the SD card.
If you have 'saved' your track on the GPS - that also is easy to download because again that is in 'user memory' and not on the card - but it won't have the timestamps you need and all in all is a rather poor record.
All this applies to the model mentioned (Etrex C type) and others of the same generation (60 series) but not to the newer Edge, Colorado, Oregon, Dakota models which have their storage organised differently.