Time Capsule: internal disk needs repair

Unfortunately, not without removing the drive. Most drive utilities, including the built-in Disk Utility on your notebook, cannot "repair" network drives ... such as the drive in your Time Capsule...and, even if it could, there's no guarantee that it would actually do so.

Regardless, you would need to remove the drive to allow any of these utilities to attempt to repair it. About all you can do with the drive installed is to use the Verify Backups option from the Time Machine icon on the macOS menu bar. To access this option, just hold down the option key before clicking on the Time Machine icon on the menu bar.

What model is the Time Capsule? Sometimes a disk error is actually something else.. like power supply but we need to know which model to help use figure out the likely cause.

Each time you reboot the TC a basic disk check is carried out.. but Apple provided just one tool that is available in Airport Utility.

You can do a full erase.. zero out data.. as Apple Speak would have it.

Warning it will fully erase any data currently on the disk.. if you have data you need to recover you MUST remove the disk from the TC.. there is nothing you can do with it inside the TC unless the disk error is false which happens when the power supply begins to fail sometimes.

That would write zeros to every track.. and it will test if the track can be read. Quick erase will just delete the indexes so is of no help.

If the disk is faulty at all.. it is unlikely to be repaired and should be replaced.. again from the model we can suggest if this is worthwhile or not.