As a teacher, I'm two minds as to what advice to give you. You face two choices:
1) Try to imitate the linking between the two words that a native speaker would likely use.
2) Don't bother. Just pronounce the final '-ed' as /t/ and move on to the following sound.
Given the scant evidence of your speech that I can hear from the audio file you posted, I lean towards recommending the second option. It's more important that you be understood than you sound like a native speaker.
And more important than the linking is that the vowel you're producing in the word 'them' is too strong. Unless you have a particular reason to stress that word, the vowel should be in a weak form.