I have accepted iCal invitations with repeating events and they have since been deleted from the iCal on my Mac but won't delete from my iPhone. Help

I experienced this issue as well.

Background:

I had opened an ICS attachment for a repeating event on my iPhone, which added the item to my phone's calendar. I did not have the option to delete the calendar entry from my phone, and the item did not appear on the calendar on my Mac. My phone is currently running iOS 7 (but the problem began quite awhile ago; I don't recall which version of iOS was installed when it started).

Solution (summary):

Create a new calendar, move the items that you wish to delete to the new calendar, then delete the new calendar

Solution (detailed steps):

1. Create a new calendar
   1. On your phone, open the calendar app
   2. Tap the "Calendars" option at the bottom of the screen
   3. Tap the "Edit" button in the top left corner
   4. Scroll to the bottom of the list and tap the "Add Calendar..." option
   5. Give your new calendar a good name, such as "Delete me"
   6. Tap "Done" in the top right corner to save the new calendar
   7. Tap "Done" in the top left corner to finish editing the list of calendars
   8. Tap "Done" to exit the list of calendars
2. Assign all calendar entries that you wish to delete to the calendar you created in step 1
   1. Tap a calendar entry that you wish to delete
   2. Tap the "Edit" button in the top right corner
   3. Scroll down until you see the Calendar field (on an iPhone or iPod it's usually just below the bottom of the screen), then tap the Calendar field to bring up the list of available calendars
   4. Tap the name of the calendar that you created in step 1 (e.g. "Delete me"); the screen should return to the main calendar entry page
   5. Tap "Done" in the top right corner of the screen. You may need to then tap the "< Day" button on the top left of the screen to return to the main calendar view
3. Repeat the instructions in step 2 for each of the calendar entries that you wish to delete
4. Delete the calendar that you created in step 2 (this will delete all calendar entries assigned to this calendar)
   1. From the main screen in the calendar app, tap the "Calendars" option at the bottom of the screen
   2. Tap the "Edit" button in the top left corner
   3. Tap the entry for the calendar that you created in step 2 (e.g. "Delete me")
   4. Scroll to the bottom of the scren and tap the "Delete Calendar" option. You should be prompted with a warning that explains that "All events associated with this calendar will also be deleted."
   5. If you're sure that the only items on this calendar are items that you wish to delete, tap the "Delete Calendar" button
   6. Tap "Done" in the top right corner to exit the Edit Calendars screen
   7. Tap "Done" to exit the list of calendars. You should now be back at the main view of the calendars app
5. Rejoice, your pesky repeating calendar events have been deleted
   1. At this point all of the items that you assigned to the deleted calendar should be gone
   2. Repeat the steps above for any entries that you missed
   3. Post another message to this thread if this did not resolve your problem

minor edit for clarity made by ScottHooley