The suffix is actually -val/-vel. With vowels. Találkoztam Annával. I met with Anna. Találkoztam Endrével. I met with Endre.
With consonants it is -al/-el und you double the consonant. (so in plural cases it is -kal/-kel)
katonákkal ... with the soldiers/ katonával ... with the soldier
"I met with the soldiers" will mean that we were in the same place together and interacted, whereas if you say "I met the soldiers" that can mean "I met with the soldiers" or "I made the acquaintance of the soldiers." Without additional context I would usually take "I met [person]" to mean the second case (that you shook hands and introduced yourselves for the first time), whereas "I met with [person]" I'd imagine you sat down and had a planned meeting, presumably with someone already known to you. My understanding is that "találkoztam" only covers the "I met with" case, so you'd never make the soldiers the object of the verb.
The past tense marker is the t after the verb stem (which is then followed by the appropriate 1st person personal ending).
Találkozom a katonákkal - I meet with the soldiers.
Találkoztam a katonákkal - I met with the soldiers.
With the verb ebédel you would have:
Ebédelek a katonákkal - I eat lunch with the soldiers.
Ebédeltem a katonákkal - I ate lunch with the soldiers.
The -t- marker is used to show the past tense in all persons. For example, 2nd person, with the verb olvas
Olvasol a gyerekekkel - You are reading with the children.
Olvastál a gyerekekkel - You were reading with the children.
(You could also translate those in English with the simple present and past, but present tense "read" looks just like past tense "read" in English, so I went with the continuous forms.)
You only use the definite conjugation if you have a definite direct object. That's the noun that gets a -t case suffix. There is none here (since you're only eating with the soldiers, and not eating the soldiers), so you use indefinite conjugation.
- Ebédelek a katonákkal.
- Ebédelem a katonákat. (not recommended)