Information Card — a notification by which an employer informs the Labour Office (Úřad práce) that they have hired a foreigner with free access to the labor market. Deadline — no later than the day the work begins.
Why it concerns you
Holders of temporary protection do not need a work permit: access to the labor market is free. But "no permit needed" does not mean "nothing needed" — the card must be submitted, and the employer does this.
It is their duty, but it officially records your legal employment. If the employer "forgets" — it is their violation, but you will have to sort it out together.
What you should do
When you get a job, calmly ask if the information card has been submitted. This is a normal question, and a reasonable employer will answer it without offense. It is especially worth asking where you are hired "quickly and without extra papers".