For what its worth, the young 20 something border officer who looks like he was born after the Yeltsin era at Domodeava airport forgot to collect my migration card a few times. I just handed the officer my passport and boarding pass. This was at the expedited lane in Domodeva airport, next to the BA lounge.
I use to go to Moscow once or twice a month, pre Crimea. I only realized that I did not surrender the migration card after I had left the Russian Federation. The officer spoke little to no English, yet managed to say " look at me " when checking my passport photo. [ "look at me", I wonder where the officer learnt that phase lol
] . Russian blog readers will understand why this is funny.
On subsequent entries into the Russian Federation, I was admitted with no problems, despite not handing in the card [ yes, I am a good boy ] and made it a point to surrender the migration card even if the officer forgot to ask, which is frequent. I think best be on the correct side of the rules. Forgetting to ask is probably due to language skills. To keep things simple and without misunderstandings, I speak English to the officers, even though I might understand their Russian.
Interpret this information however you wish, but Temedar's advice is correct. However I would go one step further to ask the assistance of the agentry / person that prepared the visa invitation for you, for assistance. That should be your primary point of contact to help you.