This study found a greater increase in BMD when taken in the morning:

"A 12-month morning teriparatide (TPTD) administration resulted in a larger increase in the lumbar spine bone mineral density (BMD) than the evening application. The results indicate that the response of bone cells to teriparatide treatment depends on dosing time."
https://pubmed.ncbi.nlm.nih.gov/22426952/#:~:text=A%2012%2Dmonth%20morning%20teriparatide,treatment%20depends%20on%20dosing%20time.