iPhone calendar

I have added Google calendar in settings. This is what a Google calendar created event looks like on my iPhone in the iPhone's calendar. There's no Edit in the upper right corner (I'm used to seeing that on other calendar events). The only way I see to try to change this kind of invitation is by "Propose New Time" - but if I do that, it sends the proposed change to the invitee who sent me this event invitation. I think it then has to be changed on that calendar by whoever manages that calendar and they have to re-send invitations to everyone on the original invite list. It doesn't seem like I can edit the event to a different date/time and have it change on the invitee's calendar.

We use gmail at work. I was hoping I could use the iPhone calendar for everything, but maybe I have to download the Google calendar app on my iPhone?

Thanks for your questions and attempts to help me. Sorry about not being clear with my earlier question.

The company uses Gmail addresses - for the company and all employees. This example was an invitation from the company calendar to me as a test to see if we could figure out why I can't edit an invitation. All their invitations have changed the default setting to allow those invited to edit the invitation (these are sales calls so sometimes the person invited to go on that sales call has to change the date or time or information about the sales call). One of my co-workers uses an Android phone and can edit the invitations, but the only way I see a possibility of editing the sales call is Propose New Time which sends an email back to the company email address with the proposed new time, whereby they have to edit it so that it's changed on the company calendar.

Should I download the Google calendar app and use that on my iPhone? I was hoping all could be done using my iPhone calendar, but maybe not? Another co-worker who uses an iPhone has the same problem. We were looking at the company calendar and when you click on the invitation itself (that the company created), it can obviously be edited from the company calendar - the invitation for the co-worker who uses an Android shows it can be edited, but my invitation, as well as the co-worker who also uses an iPhone, does NOT show the edit icon. So, even on the company end, though they created it with the default changed to anyone invited can edit the invitation, you can see that it appears the invite cannot be edited by iPhone users (apparently only those - I haven't checked with other co-workers to see if others are experiencing the same). I just found out someone else was having a problem which led me to wonder if it's a Google/iPhone calendar integration issue.