Here's what I located regarding the tilia tree. It is a type of birchwood or elm tree or sometimes called a linden tree. The article says that
A coppice of T. cordata in Westonbirt Arboretum in Gloucestershire is
estimated to be 2,000 years old. In the courtyard of the Imperial
Castle at Nuremberg is a Tilia which, by tradition recounted in 1900,
was planted by the Empress Cunigunde, the wife of Henry II of Germany
circa 1000. The Tilia of Neuenstadt am Kocher in Baden-Württemberg,
Germany, was estimated at 1000 years old when it fell
The Gamarah does not specifically state that "tilia" is "wine". It looks like you got this idea from Rash"i who defines this as "bad wine".
As Rash"i was a wine-maker, I certainly would trust his judgement regarding what is bad wine. However, I would safely assume that the term "wine" does not necessarily mean a product made from grapes. Saki, for example is a wine made from rice.
Considering that according to the article, the tillia tree existed during the time of the Gemara, it may be possible that the Gemara was referring to wine made from this plant.
As you know. most white wines today are made from grapes. If, in fact, the Gemarah's definition of "tilia" is, in fact, this tree (again, bear in mind that the Gemarah itself does not use the term yayin, even if we were to assume that in the Gemarah, yayin does mean exclusively a grape-made product. Rash"i, lived many years later than that, and, it is possible that he had a different usage of the term yayin.) is what the Gemarah meant, I think it's safe to assume that we have no concern that our wines are from the tilia tree.