Remember your hotel is legally responsible for doing this , a friend of mine recently went to bangkok main immigration office with a letter from the hotel and the officer asked for TM30 copy etc , the hotel forgot to enter the information in the system. My friend was told to come back with someone from the hotel the following day , he did and the hotel was fined 4000 baht. He then presented the TM30 and got his 90 day report
The hotel would of entered the information in the immigration system ask them for at least a screen shot of the entry made in the system , but they can print off the entry if they know how , hotels ars doing this all the time so should supply at your request