Attempting to remove Password/Pin and now have a problem.

First, be sure to back up all the user data, in case the wrong profile is deleted. If you can sign in by clicking your name in lower L corner, you're all set as an alternate User.
Next, I'm guessing the account with her picture is an MS account where she can use her email password. The one with the generic avatar and gmail (please cover up her personal email in your screenshot and re-post)is a Local acct, as is yours.
Decide which of her two accounts she can sign in on successfully and delete the other (be SURE to copy any wanted contents in Pictures, Documents, etc in the acct you want to delete to the same folders in the one you want to keep !!)
Delete the unwanted accounts using any of a number of options covered here - Delete User Account in Windows 10
Good Luck, mate.

Often you get duplicate accounts on lock screen if you have used netplwiz to set logon without password and then changed password (or changed from local account to Microsoft Account).

For example if you were logging on automatically with user "Margret" and password "Password1" and then made Margret local account into a Microsoft Account "Margret@outlook.com" with password "Password2" it will get confused.

Try going to netplwiz and toggle on and off the "Users must enter a user name and password to use this computer" box a few times (logging off in-between).

Sign in User Account Automatically at Windows 10 Startup Windows 10 Tutorials

Thank you both so much for your prompt replies. Yes I did use that netplwiz a couple of times - I also had deleted successfully a profile I made for myself a long time ago but no matter what I did I could not get rid of these other profiles that did not have my picture on. In the end I did a system restore - even tho my anti virus help people advised some time ago not to use it - don't know why - but decided it was safer for me...as I just seemed to make a further mess. THat worked thankfully.
I am reluctant to attempt to help my friend with her laptop now - are either of you familiar with the problem that some HP Laptops have that it keeps saying its the incorrect pin - its a microsoft sign in - not local user - and then it locks her out for 2 hours - I tried and got in and then next thing it would not let us in again....that was why I thought I would TRY to work out how to remove the need for a password/pin sign in.
AM I RIGHT in assuming that if I change her to a local user there is no way for her photos to be uploaded automatically to one drive?
Any other problems that will arise by being a local user?
OR - do you know how to fix this problem as her pin is correct. Not sure what to do. THank you so much.

Also as suggested - how do I remove the image that has my email address on it please?

"are either of you familiar with the problem that some HP Laptops have that it keeps saying its the incorrect pin - its a microsoft sign in - not local user - "

If System Restore worked, then create a new point (type 'create restore point' in Cortana search box, lower L) before trying all these new fixes. I have 3 HP laptops and this is NOT a brand issue but a user error. If you have a MS sign-in, verify it here - https://account.microsoft.com/account/manage-my-account
If your pass is, indeed, correct, you'll see options to edit your name (picture too), change password (can test change here, write new one down) and see the HP under 'Devices'. I would also check out 'Is your info up to date' section where you can have them text you a temp code to your phone if you can't sign in or are locked out.

AM I RIGHT in assuming that if I change her to a local user there is no way for her photos to be uploaded automatically to one drive? Any other problems that will arise by being a local user?

Yes, if the Local account sign-in is NOT a MS email. Here's a good tutorial on the differences. This covers adding another person (like you, for support) vs having her USE a Local account INSTEAD of her MS acct - Add Local Account or Microsoft Account in Windows 10

Rather than complicate things by adding more users, if the Onedrive photo issue is the only problem, here's a 30 second fix to stop it and save to This PC/Pictures instead. - Turn On or Off Auto Save Photos and Videos to OneDrive in Windows 10
You can also take the additional step of disabling Onedrive 'start with Windows' if you don't use it at all.

Also as suggested - how do I remove the image that has my email address on it please?

I see you figured that out but it would help us if you can post another after these changes, as I'm a little confused as to whether you just want the user with the picture avatar or the generic or two separate users (good to have in case the main is locked out), or what. Use the built-in Snipping tool (type in search box, lower L) which has a pen tool you can use to cross out personal name attached to gmail. You can alternately, cross out any personal info by editing the picture in Paint. Let us know if you made progress. Cheers.