DnD 5e On the Subtlety of Verbal and Material use During Spellcasting [duplicate]

In a campaign amongst my friends and myself, I am playing a divination wizard who enjoys utilizing suggestion in social activities from time-to-time. In this particular scenario, my party and I were in a were in a church speaking to a Cardinal in his office. A monk friend of mine decided to say some heretical words which prompted the Cardinal to yell "Guards!" thus beginning a train of 15 guards rushing into the room. In this time, I wanted to cast suggestion as a means of evading subsequent conflict. Whether or not my suggestion would have been seen as reasonable is not a part of this question, but instead I am interested in the manner in which the guards would have viewed this spell cast.

Suggestion, of course, is composed of a verbal component and a material component which is then followed by up to a two sentence suggestion.

The immediate feedback from the DM upon attempting to use suggestion is that the cast would be obvious to the guards as spellcasting in itself is not a secret to bystanders thus no opportunity to roll out any plays. DM ruling accepted with some pushback, but we tabled this until after the session where we basically agreed that in situations such as a busy bar or a busy marketplace I could potentially get away with pulling off a suggestion without drawing too much attention to myself. Seems reasonable to me.

Now my issue lies in how this was handled. If these guards are rushing in, certainly making some noise, they don’t necessarily know I’m a wizard before hand, and I’m not facing these guards; should my verbal and material components use be painfully obvious to the guards or is this something that can be done with some subtlety given the situation?