Help with messed up repository (one remote, two local)

[smXplorer]

I am usually doing some basic code development on one PC (A) and pushing that to bitbucket via Sourcetree.

On my production computer (B), I pull this locally and typically mostly use the code as is, occasionally fixing a few bugs and pushing back to the Bitbucket repository.

Recently, I found myself in a situation where, while on (B), I pushed some modifications to Bitbucket, only to discover that I had some pending mods on (A) as well. I committed those on A locally and tried to push that to Bitbucket, which obviously failed.

I tried some uneducated actions: pulling the remote (as the error message was suggesting this) and some additional merge of some kind, which I stupidly did not note down.

The result is that I am finding myself in the situation described below (on A), which prevents me from pushing any further modifications made on A.

Is there any simple course of action to reconcile A and the remote so that I can the pull the result to B?

Edit: 

Actually, here is the error message I get when pushing the A repo to Bitbucket in SourceTree:

git -c diff.mnemonicprefix=false -c core.quotepath=false --no-optional-locks push -v --set-upstream origin master:master
Pushing to https://bitbucket.org/XXXXXXXXXX.git
To https://bitbucket.org/XXXXXXXXXXX.git
! [rejected] master -> master (non-fast-forward)
error: failed to push some refs to 'https://bitbucket.org/XXXXXXXXXX.git'

hint: Updates were rejected because a pushed branch tip is behind its remote
hint: counterpart. Check out this branch and integrate the remote changes
hint: (e.g. 'git pull ...') before pushing again.
hint: See the 'Note about fast-forwards' in 'git push --help' for details.

Completed with errors, see above.

[smXplorer]

While I can't say that I have quite understood how this works, I managed to get out this hole by following some of the UI 's suggestions, ending up with this situation:

The lesson I draw from this is to always pull from remote before working on a repo and always push after having worked on a repo. Whichever machine you are working on. Sort of...