Don't use transaction IDs for this purpose, we've found that PayPal will send the buyer and the merchant different transaction IDs, and the number we'll have in your sales records will not be the same as the one on the buyer's receipt.
Buyers will normally see the invoice number we generate for them though. This is a very long string of characters but they could copy and paste it back to you when they send the file your way. You can then copy that same invoice number into your transaction log to verify their order.
You might find it easier just to go by their email address though, you can also look that up in your sales records to confirm their order. Then you could only use the invoice number as an emergency backup for people who are contacting you by a different email address then the one they purchased under.