Conditional Formatting / FALSE return to BLANK

I am designing a workbook of potential clients. Each potential client has a sheet. On what I'll call my "Master Sheet", I have each potential client listed by last name. What I'd like to do is the following:

If the last update to the client is over 30 days, I'd like to flag it with the word "UPDATE" and conditional formatting to make that cell red (in the cell before client's last name). If the update returns "FALSE" (i.e. less than 30 days since update), I'd like the cell to appear BLANK (as no update is needed).

So far the update formula I'm using works fine: (=IF('clientlastupdate-date'<TODAY()-30, "Update"), and I've been able to structure the conditional formatting to appear as I'd like.

My issue is the FALSE return, how do I edit this formula to return a blank cell if no update is needed? Is this possible? Please note that the last update date is coming from a cell in the corresponding client's worksheet.

(screen shot attached)

Thanks in advance for your time/help!