“Additionally, under Jewish law a convert, once converted, is considered to no longer have any relationship with his biological family. This is true to the point that under pure biblical law it is even technically permitted for a convert to marry his biological mother if she also converts. The biblical obligation of honoring one’s parents doesn’t apply to them, though by rabbinical edict some obligations apply and marriage to them is prohibited.”
Most Rabbis do tell converts that it is praiseworthy to maintain some contact with their biological family, although of course, caution must be used which is why Rabbinical guidance is needed. I am under the impression that the concept of gratitude for your parents for having brought you into this world does apply.