Thanks @ThijsDhollander, @rsmith, and @Kerstin for your help with the commands. They are extremely helpful! I managed to get the T1 aligned for 5ttgen.
I had the T1s and DTIs previously processed in Freesurfer (recon-all and dt_recon), so the DTI data were already registered to the T1 using boundary-based registration. I then used the Freesurfer’s registration to register the aparc+aseg.mgz to the preprocessed DTI.
Here are my steps, and hopefully this might be helpful for others who have already processed the T1 dataset and want to use the aparc+aseg.mgz, especially after QC and manual edits have been painstakingly done in Freesurfer. If there are any other ways to improve or correct the workflow, please let me know 
- Use a Freesurfer command to convert the registration matrix into an ITK format
lta_convert -inlta register.lta (DTI to T1 from BBR) --outitk itk.txt
- Use the transformconvert in MRtrix to convert the itk format into MRtrix format
transformconvert itk.txt itk_import Freesurfer_to_ITK_MRTRIX.txt
mrtransform aparc+aseg.mgz -linear Freesurfer_to_ITK_MRTRIX.txt aparc+aseg_to_DTI.mgz (output) -inverse -interp nearest