All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
You are not Islamically obliged to buy anything for the parents of your foster child (son from breastfeeding relation), neither travel tickets nor anything else, just as it is not an Islamic obligation to write the name of his father on the wedding invitation card. What is important is that the child should not be attributed to the husband of the breastfeeding mother; rather, he must be traced back to his father by lineage [i.e. his real biological father], whether in official documents or when introducing him.
It is not permissible to trace him back to the husband of the breastfeeding mother.
We recommend to the son, after fearing Allah, to be keen on being kind and dutiful to his parents, because being kind and dutiful to them is not waived under any circumstances even if they are non-Muslims. If they want to attend his wedding and they asked him to buy for them travel tickets for example, from his own money, or reserve a place for their residence, and he is able to do so, then he should obey them, because obeying them in matters that do not involve disobedience to Allah is considered part of being kind and dutiful to them.
Allah Knows best.