They go up and eventually will fall back down. As long as you’re burning fat, triglycerides will rise. This is why it’s not recommended to get bloodwork done during an extended fast. You won’t get accurate results.
A study was done on this. https://pubmed.ncbi.nlm.nih.gov/36296997/
40 obese people fasted for two weeks. Their triglycerides and HOMA-IR went up during the refeed, but returned to baseline after they were measured in the six-week follow up.