My Tikkun Korim has horizontal lines over some vets, tavs, and kafs that do not appear in my chumash. What do they signify?

Shalom, Thank you for your question. The letters you mentioned (vet, tav, kaf – as well as gimmel and peh) each have two pronunciations. They can be "soft" letters, such as a vet, or "hard" letters, such as bet. This depends on various rules of Hebrew grammar. The Tikun you are using probably puts a mark – the horizontal line you mentioned – over these letters to mark when they are to be pronounced softly, and when they are to be pronounced in their hard form. There is no universal standard for this marking, and different editions use slightly different signs in order to mark this out – and some editions do not mark it all, and leave the reader to use their knowledge of Hebrew grammar to work out the pronunciation. May you be successful in your Torah learning – Blessings.