King Willem III almost broke off his engagement to princess Emma of Waldeck-Pyrmont because she was friends with commoners in Arolsen (not a large town so not many high ranked people outside her close family). Do you really think he would have accepted a bride marrying into the Dutch Royal House who'd had a child out of wedlock? Im certain he would not and neither would his first wife Queen Sophie. When her husband's aunt princess Marianne got pregnant from an extra-marital affair that made the Prussian and Dutch court accept a quick divorce Sophie refused to receive or visit Marianne ever again. Marianne got the cold shoulder from her own family for quite a while and it took years for some of the family to contact her again.
Prince Frederik of the Netherlands was close to his Prussian relatives and was the father of the Queen of Sweden and Norway and grandfather of the young Danish crown princess. His niece Sophie of the Netherlands had married Carl Alexander of Saxony-Weimar-Eisenach (his sisters married two Prussian princes) and was well connected to other courts. Had they even heard a rumour they would no doubt have mentioned it.
As for what a royal suitor might overlook. Wiwill, prince of Orange once wrote home during a visit to Russia to meet a potential Imperial bride: the farmer's daughter/peasant does not want me.
Implying that he himself was looking for more than high rank and wealth.
My interpretation of the situation is that only a few inside family members knew of Thyra's pregnancy and it was not common knowledge at other European courts. I would not be surprised if even not all the siblings let alone their spouses knew about it. Outside her mother George of Greece knew and possibly Waldemar as he and Thyra were very close but unless we find letters between them referring to it we'll never know.
As we now know from surviving correspondence from past centuries, there were some fairly open “secrets” and also lesser-known “secrets” in Europe's royal courts.
What *might* have been whispered about young & available Thyra would likely not have tainted her much, if at all, in the eyes of any ambitious royal suitors.
After all, she was one of the *best-connected* royal princesses of her time: daughter and sister / sister-in-law of no less than ten current or future crowned heads: King Christian IX and Queen Louise, King George & Queen Olga, Empress Marie and Emperor Alexander III, King Frederik VIII and Queen Louise, King Edward and Queen Alexandra.
What ambitious prince could resist becoming part of that circle?